title
Coding Challenge #56: Attraction and Repulsion Forces
description
In this challenge, I create a particle system and add "attractors" simulating attraction and repulsion forces. Code: https://thecodingtrain.com/challenges/56-attraction-and-repulsion-forces
đšī¸ p5.js Web Editor Sketch: https://editor.p5js.org/codingtrain/sketches/6WL2O4vq0
đĨ Previous video: https://youtu.be/f5QBExMNB1I?list=PLRqwX-V7Uu6ZiZxtDDRCi6uhfTH4FilpH
đĨ Next video: https://youtu.be/ZiYdOwOrGyc?list=PLRqwX-V7Uu6ZiZxtDDRCi6uhfTH4FilpH
đĨ All videos: https://www.youtube.com/playlist?list=PLRqwX-V7Uu6ZiZxtDDRCi6uhfTH4FilpH
Videos:
đ Vectors Video: https://youtu.be/vqE8DMfOajk
đ Gravitational Attraction: https://thecodingtrain.com/tracks/the-nature-of-code-2/noc/2-forces/5-gravitational-attraction
đ´ Live Stream #76: https://youtu.be/OkkjlHTdLGI?t=4692
Timestamps:
00:00 Introduction to the Challenge!
02:31 Explanation of Gravitational Attraction
05:04 Create a particle and an attractor
07:26 Add physics to the particles
11:09 Explanation of force and Newton's Second Law
13:04 Create the attraction force vector
17:51 Fine tuning the attraction force
19:34 Drawing the trails of the particle
20:37 Adding multiple particles and other changes
23:08 Adding multiple attractors
27:13 More visual changes and emerging patterns
32:31 Creating attractors with the mouse
35:11 Add repulsion force
35:55 Create alternating attractors and repellers
37:59 Suggestions for improvement and tuning parameters
38:30 Adding repulsions when particle is close to the attractor
43:42 Wrapping up and more possibilities
Editing by Mathieu Blanchette
Animations by Jason Heglund
Music from Epidemic Sound
đ Website: http://thecodingtrain.com/
đž Share Your Creation! https://thecodingtrain.com/guides/passenger-showcase-guide
đŠ Suggest Topics: https://github.com/CodingTrain/Suggestion-Box
đĄ GitHub: https://github.com/CodingTrain
đŦ Discord: https://thecodingtrain.com/discord
đ Membership: http://youtube.com/thecodingtrain/join
đ Store: https://standard.tv/codingtrain
đī¸ Twitter: https://twitter.com/thecodingtrain
đ¸ Instagram: https://www.instagram.com/the.coding.train/
đĨ Coding Challenges: https://www.youtube.com/playlist?list=PLRqwX-V7Uu6ZiZxtDDRCi6uhfTH4FilpH
đĨ Intro to Programming: https://www.youtube.com/playlist?list=PLRqwX-V7Uu6Zy51Q-x9tMWIv9cueOFTFA
đ p5.js: https://p5js.org
đ p5.js Web Editor: https://editor.p5js.org/
đ Processing: https://processing.org
đ Code of Conduct: https://github.com/CodingTrain/Code-of-Conduct
This description was auto-generated. If you see a problem, please open an issue: https://github.com/CodingTrain/thecodingtrain.com/issues/new
#forces #vectors #attractionrepulsion #physics #p5js
detail
{'title': 'Coding Challenge #56: Attraction and Repulsion Forces', 'heatmap': [{'end': 627.775, 'start': 597.066, 'weight': 0.723}, {'end': 1032.13, 'start': 1004.185, 'weight': 0.714}, {'end': 1092.952, 'start': 1056.275, 'weight': 0.738}, {'end': 1227.311, 'start': 1139.341, 'weight': 0.81}], 'summary': 'Explores a coding challenge to create visually interesting attraction patterns by implementing gravitational attraction, building a basic physics engine, and simulating particle attraction with multiple attractors, demonstrating diverse visual outcomes and addressing interaction issues.', 'chapters': [{'end': 152.804, 'segs': [{'end': 38.278, 'src': 'embed', 'start': 0.149, 'weight': 0, 'content': [{'end': 2.851, 'text': 'Hello, and welcome to a coding challenge.', 'start': 0.149, 'duration': 2.702}, {'end': 6.954, 'text': 'So this coding challenge is called, I think, Attraction and Repulsion.', 'start': 2.871, 'duration': 4.083}, {'end': 9.876, 'text': "So I'm recording the intro after I did the challenge.", 'start': 7.434, 'duration': 2.442}, {'end': 13.199, 'text': 'It was kind of a mess, and I never really got to the result that I wanted.', 'start': 9.896, 'duration': 3.303}, {'end': 15.841, 'text': 'And I just sort of played around with a bunch of different possibilities.', 'start': 13.519, 'duration': 2.322}, {'end': 20.384, 'text': "So I'm asking you, the internet, to, are you the internet? I'm not sure who the internet is.", 'start': 16.101, 'duration': 4.283}, {'end': 20.964, 'text': "Maybe it's you.", 'start': 20.424, 'duration': 0.54}, {'end': 21.805, 'text': "I don't know who it is.", 'start': 21.184, 'duration': 0.621}, {'end': 27.289, 'text': "But you're watching, to take my code and hopefully expand on it and improve on it in interesting ways.", 'start': 21.845, 'duration': 5.444}, {'end': 38.278, 'text': 'So what I was imagining was creating a lot of interesting attraction patterns by looking at the trails of various objects as they move and get attracted to different attraction points within a canvas.', 'start': 27.589, 'duration': 10.689}], 'summary': "Coding challenge 'attraction and repulsion' seeks internet's help to improve code for creating attraction patterns in a canvas.", 'duration': 38.129, 'max_score': 0.149, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/OAcXnzRNiCY/pics/OAcXnzRNiCY149.jpg'}, {'end': 150.483, 'src': 'embed', 'start': 121.715, 'weight': 2, 'content': [{'end': 123.896, 'text': "And then at the end you'll look at this video's description,", 'start': 121.715, 'duration': 2.181}, {'end': 129.497, 'text': 'find the code and hopefully expand on it and make something much more beautiful and much more interesting, because I really failed at doing that.', 'start': 123.896, 'duration': 5.601}, {'end': 131.759, 'text': 'So I hope you enjoyed this coding challenge.', 'start': 129.578, 'duration': 2.181}, {'end': 136.88, 'text': 'I guess I have to, at this point, I have to blow the train whistle.', 'start': 133.239, 'duration': 3.641}, {'end': 142.181, 'text': "I have a contract, which doesn't exist, but it says in there, blow the train whistle, so that's what I've done.", 'start': 136.92, 'duration': 5.261}, {'end': 147.863, 'text': "Enjoy the coding challenge and maybe you'll still be watching at the end or in the next video, or you might run away forever and never come back,", 'start': 142.441, 'duration': 5.422}, {'end': 148.963, 'text': 'which I would totally understand.', 'start': 147.863, 'duration': 1.1}, {'end': 150.483, 'text': 'but anyway, goodbye, see you soon.', 'start': 148.963, 'duration': 1.52}], 'summary': 'A coding challenge video where the creator invites viewers to improve the code, ending with a playful train whistle.', 'duration': 28.768, 'max_score': 121.715, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/OAcXnzRNiCY/pics/OAcXnzRNiCY121715.jpg'}], 'start': 0.149, 'title': 'Attraction and repulsion coding challenge', 'summary': 'Explores a coding challenge to create visually interesting attraction patterns by looking at the trails of various objects and exploring the mechanics of vectors and forces, encouraging viewers to improve and expand on the code.', 'chapters': [{'end': 152.804, 'start': 0.149, 'title': 'Attraction and repulsion coding challenge', 'summary': 'Explores a coding challenge called attraction and repulsion, where the speaker encourages viewers to improve and expand on the code to create visually interesting attraction patterns by looking at the trails of various objects and exploring the mechanics of vectors and forces.', 'duration': 152.655, 'highlights': ['The speaker introduces a coding challenge called Attraction and Repulsion, expressing dissatisfaction with the end result and encouraging viewers to take the code and improve it. The speaker expresses disappointment with the end result of the coding challenge and urges viewers to expand and improve on the code.', 'The challenge involves creating visually interesting attraction patterns by looking at the trails of various objects and exploring the mechanics of vectors and forces. The challenge focuses on creating attraction patterns by examining the trails of objects and understanding the mechanics of vectors and forces.', 'The speaker encourages viewers to learn about how vectors work, how forces work, and how to add different objects with the mouse, with arrays, and accumulate different forces, while acknowledging making mistakes and confusion throughout. The speaker encourages viewers to learn about vectors, forces, adding objects with the mouse and arrays, and accumulating forces, while acknowledging making mistakes and confusion throughout.']}], 'duration': 152.655, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/OAcXnzRNiCY/pics/OAcXnzRNiCY149.jpg', 'highlights': ['The challenge involves creating visually interesting attraction patterns by looking at the trails of various objects and exploring the mechanics of vectors and forces.', 'The speaker encourages viewers to learn about how vectors work, how forces work, and how to add different objects with the mouse, with arrays, and accumulate different forces, while acknowledging making mistakes and confusion throughout.', 'The speaker introduces a coding challenge called Attraction and Repulsion, expressing dissatisfaction with the end result and encouraging viewers to take the code and improve it.']}, {'end': 498.415, 'segs': [{'end': 199.284, 'src': 'embed', 'start': 152.844, 'weight': 1, 'content': [{'end': 154.284, 'text': 'So actually, let me come over to the whiteboard.', 'start': 152.844, 'duration': 1.44}, {'end': 158.805, 'text': 'The first thing that I need to do, basically, this is what I need for this example.', 'start': 154.544, 'duration': 4.261}, {'end': 160.926, 'text': 'I want to have two kinds of objects in my world.', 'start': 158.865, 'duration': 2.061}, {'end': 166.84, 'text': 'I want to have something that is an attractor object.', 'start': 163.579, 'duration': 3.261}, {'end': 173.022, 'text': "And honestly, I don't think I need a full-on attractor object in this case.", 'start': 169.161, 'duration': 3.861}, {'end': 176.843, 'text': 'The attractor can actually just be a single vector.', 'start': 173.382, 'duration': 3.461}, {'end': 180.464, 'text': 'All I care about for the attractor is its xy location, where it is.', 'start': 177.063, 'duration': 3.401}, {'end': 182.065, 'text': 'So I want to have an attractor.', 'start': 180.884, 'duration': 1.181}, {'end': 184.645, 'text': "That's a thing that's drawn on the screen.", 'start': 182.085, 'duration': 2.56}, {'end': 186.446, 'text': 'And then I want to have particles.', 'start': 184.685, 'duration': 1.761}, {'end': 193.661, 'text': 'So I want a single particle which is like a dot, and I want that dot to be attracted to the attractor.', 'start': 187.639, 'duration': 6.022}, {'end': 199.284, 'text': 'And how do I want it to be attracted to the attractor? By using gravitational attraction.', 'start': 193.962, 'duration': 5.322}], 'summary': 'Creating a system with one attractor and multiple particles using gravitational attraction.', 'duration': 46.44, 'max_score': 152.844, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/OAcXnzRNiCY/pics/OAcXnzRNiCY152844.jpg'}, {'end': 339.553, 'src': 'embed', 'start': 309.894, 'weight': 5, 'content': [{'end': 310.754, 'text': "So I'm going to go over here.", 'start': 309.894, 'duration': 0.86}, {'end': 314.196, 'text': 'And I have a particle.', 'start': 311.394, 'duration': 2.802}, {'end': 322.159, 'text': "I have a separate JavaScript file called particle.js, where I'm going to create a constructor function for the particle.", 'start': 314.856, 'duration': 7.303}, {'end': 324.18, 'text': "And I'm going to just give it an x and y.", 'start': 322.439, 'duration': 1.741}, {'end': 327.882, 'text': "So the only thing I'm going to give to the particle when it starts is a location to start.", 'start': 324.18, 'duration': 3.702}, {'end': 336.109, 'text': "And I'm going to say this.pos equals create vector x comma y.", 'start': 328.402, 'duration': 7.707}, {'end': 339.553, 'text': "So now I have a particle with a position that's a vector of an x and y.", 'start': 336.109, 'duration': 3.444}], 'summary': 'A javascript file creates a particle with a position vector of x and y.', 'duration': 29.659, 'max_score': 309.894, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/OAcXnzRNiCY/pics/OAcXnzRNiCY309894.jpg'}, {'end': 426.792, 'src': 'embed', 'start': 371.769, 'weight': 0, 'content': [{'end': 383.667, 'text': "Stroke 255, stroke weight 4, and I'm going to say point attractor dot x, attractor dot y.", 'start': 371.769, 'duration': 11.898}, {'end': 385.369, 'text': "And let's just take a look at this real quick.", 'start': 383.667, 'duration': 1.702}, {'end': 388.191, 'text': "Hit refresh, and there you go, there's my attractor.", 'start': 385.929, 'duration': 2.262}, {'end': 392.013, 'text': 'The dot in the center of the window, yes.', 'start': 390.392, 'duration': 1.621}, {'end': 393.294, 'text': "Okay, so that's working.", 'start': 392.234, 'duration': 1.06}, {'end': 395.236, 'text': 'Now, what I want to do is add a particle.', 'start': 393.354, 'duration': 1.882}, {'end': 403.702, 'text': "And I want to say a particle equals a new particle, and I'm going to put it at, I don't know, 200 comma 100.", 'start': 397.117, 'duration': 6.585}, {'end': 409.091, 'text': 'And then I want to say something like particle, Particle.show.', 'start': 403.702, 'duration': 5.389}, {'end': 413.533, 'text': "Now, I have a constructor function, so that'll work.", 'start': 409.791, 'duration': 3.742}, {'end': 414.813, 'text': 'I do not have a show function.', 'start': 413.593, 'duration': 1.22}, {'end': 426.792, 'text': "So right in here, I need to say this.show equals function, and I'm just going to also do the same thing, stroke 255, stroke weight 255.", 'start': 415.134, 'duration': 11.658}], 'summary': 'Creating an attractor and particle with specific coordinates and functions.', 'duration': 55.023, 'max_score': 371.769, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/OAcXnzRNiCY/pics/OAcXnzRNiCY371769.jpg'}], 'start': 152.844, 'title': 'Implementing gravitational attraction and particle attraction', 'summary': 'Discusses the implementation of gravitational attraction, defining attractor and particle objects, calculating the force of gravity, and creating a particle and an attractor in a javascript sketch to establish an attraction function and move the particle towards the attractor.', 'chapters': [{'end': 309.734, 'start': 152.844, 'title': 'Implementing gravitational attraction', 'summary': 'Discusses the implementation of gravitational attraction, including defining attractor and particle objects, calculating the force of gravity, and exploring the relationship between force strength and distance in a simulated pixel space.', 'duration': 156.89, 'highlights': ['Defining attractor and particle objects The chapter discusses the need for attractor and particle objects in the world, with the attractor being represented by a single vector and the particles being attracted to it.', 'Calculating the force of gravity The chapter explains the formula for gravitational attraction, which includes the universal gravitational constant, mass of the objects, and distance squared, with the author simplifying the formula for the specific scenario.', 'Exploring force strength and distance relationship The author explores the impact of distance on the strength of attraction, discussing the options of making the force strength proportional or inversely proportional to distance and encourages experimentation with this concept in creative projects.']}, {'end': 498.415, 'start': 309.894, 'title': 'Particle attraction and animation', 'summary': 'Discusses creating a particle and an attractor in a javascript sketch, demonstrating their positions and establishing an attraction function to move the particle towards the attractor.', 'duration': 188.521, 'highlights': ['The chapter discusses creating a particle and an attractor in a JavaScript sketch. It covers the creation of a particle and an attractor using a constructor function and a vector position, demonstrated in a JavaScript sketch.', "Establishing an attraction function to move the particle towards the attractor. A function called 'attracted' is defined in the particle object to enable any given particle to be attracted to a specific vector, allowing for motion towards the attractor.", "Demonstrating the positions of the particle and the attractor in the sketch. The positions of the particle and the attractor are visualized in the sketch using the 'point' function and showcased with a background and stroke settings."]}], 'duration': 345.571, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/OAcXnzRNiCY/pics/OAcXnzRNiCY152844.jpg', 'highlights': ['Defining attractor and particle objects The chapter discusses the need for attractor and particle objects in the world, with the attractor being represented by a single vector and the particles being attracted to it.', 'Calculating the force of gravity The chapter explains the formula for gravitational attraction, which includes the universal gravitational constant, mass of the objects, and distance squared, with the author simplifying the formula for the specific scenario.', 'Exploring force strength and distance relationship The author explores the impact of distance on the strength of attraction, discussing the options of making the force strength proportional or inversely proportional to distance and encourages experimentation with this concept in creative projects.', 'The chapter discusses creating a particle and an attractor in a JavaScript sketch. It covers the creation of a particle and an attractor using a constructor function and a vector position, demonstrated in a JavaScript sketch.', "Establishing an attraction function to move the particle towards the attractor. A function called 'attracted' is defined in the particle object to enable any given particle to be attracted to a specific vector, allowing for motion towards the attractor.", "Demonstrating the positions of the particle and the attractor in the sketch. The positions of the particle and the attractor are visualized in the sketch using the 'point' function and showcased with a background and stroke settings."]}, {'end': 1149.911, 'segs': [{'end': 627.775, 'src': 'heatmap', 'start': 597.066, 'weight': 0.723, 'content': [{'end': 610.536, 'text': 'So now, if I were to actually give a velocity 0, comma 1, and I were to go to the sketch and also say particle.update and run this sketch,', 'start': 597.066, 'duration': 13.47}, {'end': 610.977, 'text': 'we can see.', 'start': 610.536, 'duration': 0.441}, {'end': 611.477, 'text': 'there we go.', 'start': 610.977, 'duration': 0.5}, {'end': 614.541, 'text': 'my particle is moving towards the attractor.', 'start': 611.477, 'duration': 3.064}, {'end': 619.826, 'text': 'Now, I just happened to give it a hard-coded velocity, pointed straight at it.', 'start': 614.581, 'duration': 5.245}, {'end': 627.775, 'text': 'so if I go back to the particle and I say something like you know negative one, comma zero,', 'start': 619.826, 'duration': 7.949}], 'summary': 'Particle moves towards attractor with hard-coded velocity.', 'duration': 30.709, 'max_score': 597.066, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/OAcXnzRNiCY/pics/OAcXnzRNiCY597066.jpg'}, {'end': 715.881, 'src': 'embed', 'start': 686.152, 'weight': 1, 'content': [{'end': 689.454, 'text': 'I want to have this particle be attracted to the attractor wherever it is.', 'start': 686.152, 'duration': 3.302}, {'end': 698.259, 'text': "So I need to calculate a vector that's always pointing from this object's, this particle's location towards the attractor.", 'start': 689.754, 'duration': 8.505}, {'end': 701.271, 'text': 'And how do I do that?', 'start': 699.25, 'duration': 2.021}, {'end': 709.417, 'text': 'So the easiest thing, the easiest way to get an arrow that points from one position to another position is to subtract those two positions together.', 'start': 701.672, 'duration': 7.745}, {'end': 711.038, 'text': "So this is where I'm going to start.", 'start': 709.777, 'duration': 1.261}, {'end': 715.881, 'text': 'What I need to do is write in that attract function, I need to figure out this force.', 'start': 711.258, 'duration': 4.623}], 'summary': 'Calculate a vector pointing from particle to attractor for force calculation.', 'duration': 29.729, 'max_score': 686.152, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/OAcXnzRNiCY/pics/OAcXnzRNiCY686152.jpg'}, {'end': 756.751, 'src': 'embed', 'start': 729.091, 'weight': 0, 'content': [{'end': 734.415, 'text': "Is it a weak force? Is it a strong force? The strength of it is coming from this formula that we're kind of working out over here.", 'start': 729.091, 'duration': 5.324}, {'end': 737.157, 'text': "But beyond that, I'm saying it's a force.", 'start': 734.735, 'duration': 2.422}, {'end': 744.427, 'text': "And if I come over here position, velocity and acceleration, what's the relationship of force to position, velocity and acceleration?", 'start': 738.345, 'duration': 6.082}, {'end': 747.848, 'text': 'Well, you might be familiar with Isaac Newton.', 'start': 744.467, 'duration': 3.381}, {'end': 749.169, 'text': "And there's a bunch of laws.", 'start': 748.248, 'duration': 0.921}, {'end': 751.629, 'text': "I'm sure they're all very important and interesting.", 'start': 749.189, 'duration': 2.44}, {'end': 756.751, 'text': "But the law that I'm interested in is force equals mass times acceleration.", 'start': 751.95, 'duration': 4.801}], 'summary': 'Exploring the relationship between force, mass, and acceleration in physics.', 'duration': 27.66, 'max_score': 729.091, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/OAcXnzRNiCY/pics/OAcXnzRNiCY729091.jpg'}, {'end': 791.482, 'src': 'embed', 'start': 766.955, 'weight': 2, 'content': [{'end': 773.578, 'text': 'So force is a vector that causes a mass, a force is a vector that causes an object with mass to accelerate.', 'start': 766.955, 'duration': 6.623}, {'end': 779.261, 'text': 'And so we can actually just if I can figure out this attraction force, then I can just put that right into acceleration,', 'start': 773.859, 'duration': 5.402}, {'end': 782.583, 'text': 'and our simulation is going to do exactly what we want it to do, I hope.', 'start': 779.261, 'duration': 3.322}, {'end': 785.075, 'text': "Okay, so I'm coming back over here.", 'start': 783.433, 'duration': 1.642}, {'end': 789.079, 'text': 'Use the force, I think is the proper terminology here.', 'start': 785.896, 'duration': 3.183}, {'end': 791.482, 'text': 'Use the force.', 'start': 790.061, 'duration': 1.421}], 'summary': 'Force is a vector that causes mass to accelerate for simulation.', 'duration': 24.527, 'max_score': 766.955, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/OAcXnzRNiCY/pics/OAcXnzRNiCY766955.jpg'}, {'end': 925.725, 'src': 'embed', 'start': 893.352, 'weight': 4, 'content': [{'end': 895.473, 'text': 'So I want to have an inversely proportional distance.', 'start': 893.352, 'duration': 2.121}, {'end': 897.315, 'text': "So let's figure out how we can do that.", 'start': 895.854, 'duration': 1.461}, {'end': 905.141, 'text': "Now, one thing that's nice here is this vector that points all the way from one object to the other That is the distance.", 'start': 897.655, 'duration': 7.486}, {'end': 911.402, 'text': 'And actually, I can just get distance squared is the direction.', 'start': 905.421, 'duration': 5.981}, {'end': 913.283, 'text': 'That vector, the length of it is distance.', 'start': 911.723, 'duration': 1.56}, {'end': 920.444, 'text': "And if I want distance squared, there's actually a function, I believe, in P5 called magSq for magnitude squared.", 'start': 913.343, 'duration': 7.101}, {'end': 925.725, 'text': "So this is giving me that value, distance squared, that's on the bottom of our calculation.", 'start': 920.784, 'duration': 4.941}], 'summary': 'Discussing inversely proportional distance using vector and p5 function.', 'duration': 32.373, 'max_score': 893.352, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/OAcXnzRNiCY/pics/OAcXnzRNiCY893352.jpg'}, {'end': 1032.13, 'src': 'heatmap', 'start': 1004.185, 'weight': 0.714, 'content': [{'end': 1007.708, 'text': "So ultimately I'm starting with a force that's the full distance.", 'start': 1004.185, 'duration': 3.523}, {'end': 1012.371, 'text': "then I'm getting the distance squared, making up a gravitational constant, calculating the strength and setting it.", 'start': 1007.708, 'duration': 4.663}, {'end': 1015.593, 'text': 'And now what do I do? Acceleration equals force.', 'start': 1012.411, 'duration': 3.182}, {'end': 1019.782, 'text': "So in this case, let's take a look and see what we've got.", 'start': 1016.84, 'duration': 2.942}, {'end': 1032.13, 'text': 'So now, if I call particle attracted, particle update, and particle show, I should calculate a force in the attracted function.', 'start': 1020.182, 'duration': 11.948}], 'summary': 'Calculating force, distance squared, and acceleration for particle attraction.', 'duration': 27.945, 'max_score': 1004.185, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/OAcXnzRNiCY/pics/OAcXnzRNiCY1004185.jpg'}, {'end': 1092.952, 'src': 'heatmap', 'start': 1056.275, 'weight': 0.738, 'content': [{'end': 1060.337, 'text': "Let's just hard code the strength for a second as one.", 'start': 1056.275, 'duration': 4.062}, {'end': 1062.278, 'text': "Oh, it's working.", 'start': 1061.758, 'duration': 0.52}, {'end': 1064.079, 'text': 'So there we go.', 'start': 1063.538, 'duration': 0.541}, {'end': 1067.38, 'text': 'We can see now that it is experiencing that attraction.', 'start': 1064.259, 'duration': 3.121}, {'end': 1073.083, 'text': "It's just, I gotta really think about the sort of scaling of this.", 'start': 1067.82, 'duration': 5.263}, {'end': 1076.017, 'text': "So it's very, very weak.", 'start': 1074.235, 'duration': 1.782}, {'end': 1081.001, 'text': "Do you see how it's moving just a little bit? Now it's getting closer, so it's going to get stronger and stronger.", 'start': 1076.037, 'duration': 4.964}, {'end': 1084.284, 'text': 'So this is really like, I got to really start tuning stuff here.', 'start': 1081.201, 'duration': 3.083}, {'end': 1092.952, 'text': "And one thing that I'm going to do I think that's really going to help things a little bit is one thing I could do is I could just you know,", 'start': 1084.344, 'duration': 8.608}], 'summary': 'Experimenting with strength scaling, observing weak attraction, planning tuning adjustments.', 'duration': 36.677, 'max_score': 1056.275, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/OAcXnzRNiCY/pics/OAcXnzRNiCY1056275.jpg'}], 'start': 498.876, 'title': 'Building a basic physics engine and calculating gravitational force', 'summary': 'Covers building a basic physics engine using euler integration to understand position, velocity, and acceleration of a particle, and discusses gravitational force calculation using the formula of g divided by distance squared, emphasizing the need to constrain the distance squared value.', 'chapters': [{'end': 867.596, 'start': 498.876, 'title': 'Physics engine basics', 'summary': 'Covers building a basic physics engine using euler integration, discussing position, velocity, and acceleration of a particle, and understanding the force of attraction towards an attractor.', 'duration': 368.72, 'highlights': ['The chapter covers building a basic physics engine using Euler integration. The speaker discusses using Euler integration to calculate the rate of change of position over time and demonstrates integrating position and velocity in a simple way.', 'Discusses position, velocity, and acceleration of a particle in the physics engine. The speaker explains the concepts of position, velocity, and acceleration, and demonstrates how to add velocity to position and acceleration to velocity in the update function.', 'Understanding the force of attraction towards an attractor. The speaker explains the concept of force as a vector that causes an object with mass to accelerate and discusses the calculation of the force pointing from the particle to the attractor.']}, {'end': 1149.911, 'start': 867.877, 'title': 'Gravitational force calculation', 'summary': 'Explains the calculation of gravitational force between two objects, using a formula of g divided by distance squared to determine the force, and the need to constrain the distance squared value to prevent extreme force values.', 'duration': 282.034, 'highlights': ['The formula g divided by distance squared is used to calculate the magnitude of the force, with the need to adjust the gravitational constant and distance squared to control the strength of the force. The formula g divided by distance squared is utilized to calculate the magnitude of the force, with the need to adjust the gravitational constant and distance squared to control the strength of the force.', 'The importance of constraining the distance squared value is emphasized to prevent extreme force values and uncontrollable movements, with a suggested range of values for the constraint. The importance of constraining the distance squared value is emphasized to prevent extreme force values and uncontrollable movements, with a suggested range of values for the constraint.', 'The reference to the Apollo moon missions is made to illustrate the extreme effects of uncontrolled force and the need for proper calculations in physics. The reference to the Apollo moon missions is made to illustrate the extreme effects of uncontrolled force and the need for proper calculations in physics.']}], 'duration': 651.035, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/OAcXnzRNiCY/pics/OAcXnzRNiCY498876.jpg', 'highlights': ['The chapter covers building a basic physics engine using Euler integration.', 'The speaker explains the concepts of position, velocity, and acceleration.', 'The speaker discusses the calculation of the force pointing from the particle to the attractor.', 'The formula g divided by distance squared is used to calculate the magnitude of the force.', 'The importance of constraining the distance squared value is emphasized to prevent extreme force values and uncontrollable movements.', 'The reference to the Apollo moon missions is made to illustrate the extreme effects of uncontrolled force.']}, {'end': 1376.211, 'segs': [{'end': 1215.76, 'src': 'embed', 'start': 1172.18, 'weight': 0, 'content': [{'end': 1178.262, 'text': "Okay, so now let's try to do some stuff that's a little bit more interesting.", 'start': 1172.18, 'duration': 6.082}, {'end': 1185.024, 'text': 'So for example, let me at least give this vector a random velocity to start.', 'start': 1178.682, 'duration': 6.342}, {'end': 1189.212, 'text': "And we'll see.", 'start': 1188.792, 'duration': 0.42}, {'end': 1194.197, 'text': "So now it actually has a random velocity to start, so it's not pointing directly at it.", 'start': 1189.273, 'duration': 4.924}, {'end': 1198.641, 'text': 'And the other thing that I want to do I think which would be interesting to see is kind of draw some trails.', 'start': 1194.638, 'duration': 4.003}, {'end': 1201.204, 'text': "So I'm going to put background here.", 'start': 1199.542, 'duration': 1.662}, {'end': 1205.274, 'text': "And so we're going to see sort of its path a little bit more.", 'start': 1202.893, 'duration': 2.381}, {'end': 1210.637, 'text': "So now what we've got is a single particle drawing a path as it kind of orbits us.", 'start': 1205.634, 'duration': 5.003}, {'end': 1215.76, 'text': 'Now interestingly enough, another code challenge I wanted to do today was this rose petal challenge.', 'start': 1210.657, 'duration': 5.103}], 'summary': 'A single particle with random velocity is drawing a path and orbits as part of an interesting coding challenge.', 'duration': 43.58, 'max_score': 1172.18, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/OAcXnzRNiCY/pics/OAcXnzRNiCY1172180.jpg'}], 'start': 1149.911, 'title': 'Particle attraction and motion', 'summary': 'Explores the behavior of a single particle attracted to a specific attractor, demonstrating random velocity and path drawing, and creating a simulation of particle attraction with 50 particles, resulting in different patterns due to slightly different initial velocities, and a uniform pattern with the introduction of constraints.', 'chapters': [{'end': 1215.76, 'start': 1149.911, 'title': 'Particle attraction and motion', 'summary': 'Explores the behavior of a single particle attracted to a specific attractor, demonstrating random velocity and path drawing, with a hint towards a rose petal challenge.', 'duration': 65.849, 'highlights': ['The attraction force between the particle and attractor is explained, showcasing interesting behavior despite minimal actions taken.', "Demonstrating the impact of providing the vector with a random velocity, altering the particle's initial direction towards the attractor.", "The concept of drawing trails is introduced, enhancing the visualization of the particle's path as it orbits around the attractor.", 'A hint is given about the rose petal challenge, indicating a upcoming coding challenge related to this topic.']}, {'end': 1376.211, 'start': 1216.02, 'title': 'Particle attraction simulation', 'summary': 'Explores creating a simulation of particle attraction with 50 particles all starting in the same spot and showing different patterns due to slightly different initial velocities, resulting in a uniform pattern with the introduction of constraints.', 'duration': 160.191, 'highlights': ['Creating a simulation of particle attraction with 50 particles all starting in the same spot.', 'Particles showing different patterns due to slightly different initial velocities.', 'Resulting in a uniform pattern with the introduction of constraints.']}], 'duration': 226.3, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/OAcXnzRNiCY/pics/OAcXnzRNiCY1149911.jpg', 'highlights': ['Creating a simulation of particle attraction with 50 particles all starting in the same spot.', 'Particles showing different patterns due to slightly different initial velocities.', "The concept of drawing trails is introduced, enhancing the visualization of the particle's path as it orbits around the attractor.", 'The attraction force between the particle and attractor is explained, showcasing interesting behavior despite minimal actions taken.']}, {'end': 1619.306, 'segs': [{'end': 1452.62, 'src': 'embed', 'start': 1377.471, 'weight': 0, 'content': [{'end': 1380.734, 'text': 'So you can see here now everything is circling and being attracted.', 'start': 1377.471, 'duration': 3.263}, {'end': 1384.212, 'text': "Okay, I don't know if I actually like it.", 'start': 1381.73, 'duration': 2.482}, {'end': 1385.272, 'text': "It's kind of a bit of a mess now.", 'start': 1384.232, 'duration': 1.04}, {'end': 1387.353, 'text': 'I almost liked it better when it was much more uniform.', 'start': 1385.292, 'duration': 2.061}, {'end': 1395.498, 'text': 'But what I would like to do now is add multiple attractors in multiple places and see how that works.', 'start': 1388.654, 'duration': 6.844}, {'end': 1403.984, 'text': "So let's go back first of all to just a single particle and have the particle once again have very little alpha.", 'start': 1395.999, 'duration': 7.985}, {'end': 1409.063, 'text': "And we can see here's my single particle being attracted to this particular attraction point.", 'start': 1404.878, 'duration': 4.185}, {'end': 1411.847, 'text': 'Now what I want to do is add an array of attractors.', 'start': 1409.464, 'duration': 2.383}, {'end': 1417.594, 'text': "So I'm going to go to the sketch and I'm going to say attractors equals an array.", 'start': 1413.669, 'duration': 3.925}, {'end': 1423.542, 'text': "And now I'm going to say also the same exact thing for the attractors.", 'start': 1418.615, 'duration': 4.927}, {'end': 1436.358, 'text': "What I want to do is say attractors, dot, push, create vector, and here I'm just going to give them a random location, random with random height.", 'start': 1425.565, 'duration': 10.793}, {'end': 1438.9, 'text': 'Okay so now here.', 'start': 1436.358, 'duration': 2.542}, {'end': 1452.62, 'text': 'I want this exact loop attractors and I want to say attractors index i and attractors index i.', 'start': 1438.92, 'duration': 13.7}], 'summary': 'Experimenting with adding multiple attractors in different locations to observe their effect on particle movement.', 'duration': 75.149, 'max_score': 1377.471, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/OAcXnzRNiCY/pics/OAcXnzRNiCY1377471.jpg'}, {'end': 1593.425, 'src': 'embed', 'start': 1566.391, 'weight': 4, 'content': [{'end': 1570.754, 'text': "So you can't just say, set the acceleration to this attraction, set the acceleration to this attraction, to this one, to this one.", 'start': 1566.391, 'duration': 4.363}, {'end': 1572.115, 'text': "I've just got the last one.", 'start': 1571.034, 'duration': 1.081}, {'end': 1573.896, 'text': 'I need to add them all together.', 'start': 1572.395, 'duration': 1.501}, {'end': 1575.537, 'text': 'This is known as force accumulation.', 'start': 1573.936, 'duration': 1.601}, {'end': 1579.1, 'text': "So it's really as simple as me saying acceleration.addForce.", 'start': 1575.878, 'duration': 3.222}, {'end': 1581.141, 'text': "Now, there's another issue here.", 'start': 1579.6, 'duration': 1.541}, {'end': 1588.563, 'text': 'The way that force accumulation works is at every moment in time, we start from no acceleration and add all the forces together.', 'start': 1581.481, 'duration': 7.082}, {'end': 1589.424, 'text': 'Then we move.', 'start': 1588.863, 'duration': 0.561}, {'end': 1593.425, 'text': 'Then we start over from no acceleration and add all the forces together.', 'start': 1589.904, 'duration': 3.521}], 'summary': 'Force accumulation involves adding all forces to calculate acceleration for movement.', 'duration': 27.034, 'max_score': 1566.391, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/OAcXnzRNiCY/pics/OAcXnzRNiCY1566391.jpg'}], 'start': 1377.471, 'title': 'Attractors, particles, and force accumulation', 'summary': 'Explores adding multiple attractors to observe their impact on particle behavior, creating diverse visual outcomes. demonstrates creating attractor particles and addressing their interaction issues. it also explains force accumulation in physics and the resulting acceleration.', 'chapters': [{'end': 1452.62, 'start': 1377.471, 'title': 'Attractors and multiple particles', 'summary': 'Explores the concept of adding multiple attractors in various locations to observe their impact on the behaviour of particles, with a focus on creating a more dynamic and diverse visual outcome.', 'duration': 75.149, 'highlights': ["The process involves adding an array of attractors and creating multiple attractors in different locations to observe their influence on the particles' movement and visual outcome.", 'The initial observation of the system reveals a dynamic and evolving behavior as the particles are attracted to multiple points, resulting in a more diverse and visually appealing pattern.', 'The experiment aims to assess the impact of adding multiple attractors on the uniformity and overall aesthetic of the visual representation, indicating a shift towards a more dynamic and less uniform outcome.', 'The exploration emphasizes the use of attractors to manipulate the movement and visual arrangement of particles, offering potential for creating engaging and dynamic visual compositions.']}, {'end': 1543.73, 'start': 1452.62, 'title': 'Attractor particle interaction', 'summary': 'Demonstrates the process of creating attractor particles and addressing the issue of particles being attracted to only the last attractor instead of all of them, while generating a random assortment of attractor dots at different spots.', 'duration': 91.11, 'highlights': ['The chapter demonstrates the process of creating attractor particles and addressing the issue of particles being attracted to only the last attractor instead of all of them.', 'The code is modified to generate a random assortment of attractor dots at different spots each time the page is refreshed.', 'The process involves looping through attractors and particles to have the particles accumulate their attraction to all of the points.']}, {'end': 1619.306, 'start': 1543.97, 'title': 'Force accumulation in physics', 'summary': 'Explains force accumulation in physics, highlighting the need to add all forces together to determine resulting acceleration, the concept of force accumulation, and the method of clearing acceleration to zero after each calculation.', 'duration': 75.336, 'highlights': ['The resulting acceleration is the sum of all forces at play, emphasizing the need to add all forces together for accurate calculation.', 'Force accumulation is described as the process of adding all forces together at every moment in time, before moving, illustrating the continuous nature of this calculation.', 'The method of clearing acceleration to zero involves multiplying the acceleration vector by zero, effectively zeroing out all components, providing a quick and efficient solution for resetting acceleration.']}], 'duration': 241.835, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/OAcXnzRNiCY/pics/OAcXnzRNiCY1377471.jpg', 'highlights': ["The process involves adding an array of attractors and creating multiple attractors in different locations to observe their influence on the particles' movement and visual outcome.", 'The exploration emphasizes the use of attractors to manipulate the movement and visual arrangement of particles, offering potential for creating engaging and dynamic visual compositions.', 'The initial observation of the system reveals a dynamic and evolving behavior as the particles are attracted to multiple points, resulting in a more diverse and visually appealing pattern.', 'The experiment aims to assess the impact of adding multiple attractors on the uniformity and overall aesthetic of the visual representation, indicating a shift towards a more dynamic and less uniform outcome.', 'The resulting acceleration is the sum of all forces at play, emphasizing the need to add all forces together for accurate calculation.', 'The method of clearing acceleration to zero involves multiplying the acceleration vector by zero, effectively zeroing out all components, providing a quick and efficient solution for resetting acceleration.', 'The process involves looping through attractors and particles to have the particles accumulate their attraction to all of the points.', 'The code is modified to generate a random assortment of attractor dots at different spots each time the page is refreshed.', 'Force accumulation is described as the process of adding all forces together at every moment in time, before moving, illustrating the continuous nature of this calculation.', 'The chapter demonstrates the process of creating attractor particles and addressing the issue of particles being attracted to only the last attractor instead of all of them.']}, {'end': 2700.496, 'segs': [{'end': 1732.487, 'src': 'embed', 'start': 1674.759, 'weight': 3, 'content': [{'end': 1680.003, 'text': "In the chat, I'm seeing the comment, the forces are too weak for the far away attractors.", 'start': 1674.759, 'duration': 5.244}, {'end': 1682.385, 'text': 'So that certainly makes a big difference here.', 'start': 1680.243, 'duration': 2.142}, {'end': 1689.931, 'text': 'What I would like to actually see is a different way, I want to see this layer itself much more slowly over time.', 'start': 1682.585, 'duration': 7.346}, {'end': 1691.332, 'text': 'So a couple things.', 'start': 1690.712, 'duration': 0.62}, {'end': 1694.515, 'text': 'One is, I would prefer not to actually draw the attractors.', 'start': 1691.532, 'duration': 2.983}, {'end': 1699.323, 'text': "So let's not bother to draw the attractors.", 'start': 1697.321, 'duration': 2.002}, {'end': 1701.265, 'text': "Let's go back to the particles.", 'start': 1699.803, 'duration': 1.462}, {'end': 1706.489, 'text': "And one thing that I want to do is I want to create a vector that's its previous position.", 'start': 1701.645, 'duration': 4.844}, {'end': 1720.842, 'text': "And then each time after it's drawn, I want to set this.previous.x equals this.pos.x.", 'start': 1711.354, 'duration': 9.488}, {'end': 1722.624, 'text': 'I want to save its last position.', 'start': 1720.862, 'duration': 1.762}, {'end': 1732.487, 'text': 'this.previous.y equals this.pos.y because I think it might be nice to actually connect its previous location with a line.', 'start': 1724.38, 'duration': 8.107}], 'summary': 'Adjust layer speed, skip drawing attractors, connect previous positions with lines', 'duration': 57.728, 'max_score': 1674.759, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/OAcXnzRNiCY/pics/OAcXnzRNiCY1674759.jpg'}, {'end': 1950.441, 'src': 'embed', 'start': 1893.669, 'weight': 0, 'content': [{'end': 1896.01, 'text': "Let's have them, I just want to sort of see now back to the middle.", 'start': 1893.669, 'duration': 2.341}, {'end': 1903.795, 'text': "And then let's give them a little initial velocity.", 'start': 1900.793, 'duration': 3.002}, {'end': 1916.304, 'text': "So let's try this, oops, where did I miss a, I missed something, I missed a parentheses.", 'start': 1907.401, 'duration': 8.903}, {'end': 1926.087, 'text': "So yeah, so you can see that I'm going to get some interesting kind of regularish patterns just based on,", 'start': 1918.864, 'duration': 7.223}, {'end': 1933.167, 'text': 'based on the kind of initial arrangement of the particle of those attractors themselves.', 'start': 1928.342, 'duration': 4.825}, {'end': 1936.19, 'text': 'And this is kind of what I was hoping to kind of see.', 'start': 1933.187, 'duration': 3.003}, {'end': 1945.998, 'text': "Now there's so much more you could do with this if you're more thoughtful about about how you arrange the attractors,", 'start': 1936.37, 'duration': 9.628}, {'end': 1950.441, 'text': 'how you set the initial conditions, so many more possibilities here.', 'start': 1945.998, 'duration': 4.443}], 'summary': 'Demonstration of generating patterns based on initial arrangements and attractors.', 'duration': 56.772, 'max_score': 1893.669, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/OAcXnzRNiCY/pics/OAcXnzRNiCY1893669.jpg'}], 'start': 1619.306, 'title': 'Particle simulations', 'summary': 'Explores the simulation of particle attraction and the creation of particle simulations with attractors and repellers, observing unexpected results of 10 particles being attracted and the impact of 500 particles added to the system.', 'chapters': [{'end': 1674.139, 'start': 1619.306, 'title': 'Particle attraction simulation', 'summary': 'Explores the simulation of particle attraction, starting with all particles at the same location and observing the unexpected result of 10 particles being attracted to each other.', 'duration': 54.833, 'highlights': ['Observation of 10 particles being attracted to each other, resulting in an unexpected outcome.', 'Experimenting with starting all particles at the same location and observing the simulation.', 'Speculation on the impact of having only two attraction points for clarity in understanding the particle behavior.']}, {'end': 2700.496, 'start': 1674.759, 'title': 'Particle attractors and repellers', 'summary': 'Explores the creation of particle simulations with attractors and repellers, experimenting with various forces and arrangements to produce dynamic patterns and behaviors, with 500 particles added to the system to observe the impact.', 'duration': 1025.737, 'highlights': ['Creation of Particle Path Visualization The speaker discusses the process of connecting particle paths with lines to enhance visualization, emphasizing the improvement in clarity when the stroke weight is reduced to one and the alpha is increased, ultimately leading to the observation of clearer particle paths.', "Attractors' Influence on Particle Patterns The speaker experiments with the impact of attractors on particle behavior, observing the emergence of more regular patterns as 500 particles are added to the system, highlighting the need for tuning and exploration of attractor arrangements for varied visual outcomes.", "Dynamic Behavior of Particle System The speaker explores the concept of dynamic behavior in the particle system, discussing the potential for altering the attractors' positions using the mouse, resulting in the observation of various possibilities and patterns in the system.", 'Experimentation with Attractors and Repellers The speaker delves into the concept of repulsive forces by altering the attraction function, leading to the observation of particles being repelled by attractors at close proximity, and discusses the potential for creating varied behaviors and visual systems through force manipulation.']}], 'duration': 1081.19, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/OAcXnzRNiCY/pics/OAcXnzRNiCY1619306.jpg', 'highlights': ['Observation of 10 particles being attracted to each other, resulting in an unexpected outcome.', 'Experimenting with starting all particles at the same location and observing the simulation.', 'Speculation on the impact of having only two attraction points for clarity in understanding the particle behavior.', 'Creation of Particle Path Visualization The speaker discusses the process of connecting particle paths with lines to enhance visualization, emphasizing the improvement in clarity when the stroke weight is reduced to one and the alpha is increased, ultimately leading to the observation of clearer particle paths.', "Attractors' Influence on Particle Patterns The speaker experiments with the impact of attractors on particle behavior, observing the emergence of more regular patterns as 500 particles are added to the system, highlighting the need for tuning and exploration of attractor arrangements for varied visual outcomes.", "Dynamic Behavior of Particle System The speaker explores the concept of dynamic behavior in the particle system, discussing the potential for altering the attractors' positions using the mouse, resulting in the observation of various possibilities and patterns in the system.", 'Experimentation with Attractors and Repellers The speaker delves into the concept of repulsive forces by altering the attraction function, leading to the observation of particles being repelled by attractors at close proximity, and discusses the potential for creating varied behaviors and visual systems through force manipulation.']}], 'highlights': ["The process involves adding an array of attractors and creating multiple attractors in different locations to observe their influence on the particles' movement and visual outcome.", 'The exploration emphasizes the use of attractors to manipulate the movement and visual arrangement of particles, offering potential for creating engaging and dynamic visual compositions.', 'The initial observation of the system reveals a dynamic and evolving behavior as the particles are attracted to multiple points, resulting in a more diverse and visually appealing pattern.', 'The experiment aims to assess the impact of adding multiple attractors on the uniformity and overall aesthetic of the visual representation, indicating a shift towards a more dynamic and less uniform outcome.', 'The resulting acceleration is the sum of all forces at play, emphasizing the need to add all forces together for accurate calculation.', 'The method of clearing acceleration to zero involves multiplying the acceleration vector by zero, effectively zeroing out all components, providing a quick and efficient solution for resetting acceleration.', 'The process involves looping through attractors and particles to have the particles accumulate their attraction to all of the points.', 'The code is modified to generate a random assortment of attractor dots at different spots each time the page is refreshed.', 'Force accumulation is described as the process of adding all forces together at every moment in time, before moving, illustrating the continuous nature of this calculation.', 'The chapter demonstrates the process of creating attractor particles and addressing the issue of particles being attracted to only the last attractor instead of all of them.']}