title

Coding the Collatz Conjecture

description

It's the second episode of Coding in the Cabana! Here I attempt to visualize the Collatz Conjecture in Processing. Code: https://thecodingtrain.com/challenges/c2-collatz-conjecture
đšī¸ p5.js Web Editor Sketch: https://editor.p5js.org/codingtrain/sketches/XjLDE7gu6
đĨ All videos: https://www.youtube.com/playlist?list=PLRqwX-V7Uu6ZiZxtDDRCi6uhfTH4FilpH
References:
đ Collatz Conjecture Wikipedia: https://en.wikipedia.org/wiki/Collatz_conjecture
đģ Collatz Graph: All Numbers Lead to One: https://www.jasondavies.com/collatz-graph/
đģ Trying to visualize the Collatz conjecture: http://mathematica.stackexchange.com/questions/85718/trying-to-visualize-the-collatz-conjecture
đž Primitive Data Types in Java (more information about the long type): https://docs.oracle.com/javase/tutorial/java/nutsandbolts/datatypes.html
Videos:
đĨ Collatz Conjecture in Color: https://www.youtube.com/watch?v=LqKpkdRRLZw
đĨ Golan Levin's Modulo Operator video: https://www.youtube.com/watch?v=r5Iy3v1co0A
đĨ UNCRACKABLE? The Collatz Conjecture: https://www.youtube.com/watch?v=5mFpVDpKX70
Related Coding Challenges:
đ #14 Recursive Fractal Trees: https://youtu.be/0jjeOYMjmDU
Timestamps:
0:00 The Collatz Conjecture
4:10 Programming in Processing
6:46 Checking The Number of Steps
9:23 Visualizing The Collatz Conjecture
20:44 Rendering to a PDF File
22:24 Conclusions and Goodbyes
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
#collatzconjecture #modulo #processing

detail

{'title': 'Coding the Collatz Conjecture', 'heatmap': [{'end': 353.076, 'start': 330.318, 'weight': 0.786}, {'end': 1347.42, 'start': 1331.208, 'weight': 1}], 'summary': 'Explores the collatz conjecture, demonstrating the process with 111 steps for the number 5, visualizes the conjecture using processing, successfully visualizes numbers up to 10,000, and discusses creating sequences, exploring number patterns, and optimizing the visualization for controlled results.', 'chapters': [{'end': 209.215, 'segs': [{'end': 67.616, 'src': 'embed', 'start': 36.772, 'weight': 0, 'content': [{'end': 38.493, 'text': 'And the number sequence goes like this.', 'start': 36.772, 'duration': 1.721}, {'end': 40.215, 'text': 'Take any number n.', 'start': 38.674, 'duration': 1.541}, {'end': 44.178, 'text': 'If the number is even, set it equal to itself divided by 2.', 'start': 40.215, 'duration': 3.963}, {'end': 48.942, 'text': 'If the number is odd, set it equal to itself times 3 plus 1.', 'start': 44.178, 'duration': 4.764}, {'end': 55.687, 'text': "So why is this conjecture, why is this sequence interesting, meaningful, mysterious? Let's start with a number.", 'start': 48.942, 'duration': 6.745}, {'end': 58.689, 'text': "Let's say I'm going to start with the number 5.", 'start': 55.767, 'duration': 2.922}, {'end': 60.311, 'text': 'So following this, 5 is odd.', 'start': 58.689, 'duration': 1.622}, {'end': 61.912, 'text': 'Multiply it by 3.', 'start': 60.351, 'duration': 1.561}, {'end': 63.713, 'text': '15, add 1.', 'start': 61.912, 'duration': 1.801}, {'end': 64.953, 'text': 'I get 16.', 'start': 63.713, 'duration': 1.24}, {'end': 67.616, 'text': "OK Ah, that's even divided by 2.", 'start': 64.953, 'duration': 2.663}], 'summary': 'The sequence involves dividing even numbers by 2 and multiplying odd numbers by 3 and adding 1, leading to a pattern of numbers.', 'duration': 30.844, 'max_score': 36.772, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/EYLWxwo1Ed8/pics/EYLWxwo1Ed836772.jpg'}, {'end': 140.439, 'src': 'embed', 'start': 117.335, 'weight': 3, 'content': [{'end': 124.916, 'text': 'So this idea was originally suggested as a topic suggestion on August 8, 2016.', 'start': 117.335, 'duration': 7.581}, {'end': 131.198, 'text': "And there's some wonderful links here that I'll include in this video's description for you to look at and see different code examples and visualizations of it.", 'start': 124.916, 'duration': 6.282}, {'end': 132.598, 'text': "I'm going to attempt to do my own here.", 'start': 131.258, 'duration': 1.34}, {'end': 140.439, 'text': 'And what I am looking and hoping to create is inspired by the number file video about the Collatz conjecture,', 'start': 132.978, 'duration': 7.461}], 'summary': "I'll attempt to create my own visualization of the collatz conjecture, inspired by the number file video.", 'duration': 23.104, 'max_score': 117.335, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/EYLWxwo1Ed8/pics/EYLWxwo1Ed8117335.jpg'}, {'end': 209.215, 'src': 'embed', 'start': 163.927, 'weight': 1, 'content': [{'end': 168.109, 'text': "But you'll also reach 22 if you start with the number 18.", 'start': 163.927, 'duration': 4.182}, {'end': 176.034, 'text': 'kind of visualize as this branch, this graph, this tree all converging eventually every sequence all the way down to 1.', 'start': 168.109, 'duration': 7.925}, {'end': 179.936, 'text': "But I'm here in the cabana in the sun with the garden outside.", 'start': 176.034, 'duration': 3.902}, {'end': 189.842, 'text': "And I want to see, I'm inspired by this particular number file video, which creates a visualization of the Kolatz conjecture that looks like this.", 'start': 180.696, 'duration': 9.146}, {'end': 192.103, 'text': "It's like seaweed or a plant.", 'start': 189.922, 'duration': 2.181}, {'end': 193.164, 'text': "It's so organic.", 'start': 192.323, 'duration': 0.841}, {'end': 198.467, 'text': 'Why and how out of this very mathematical algorithm Do we get this seaweed-like pattern?', 'start': 193.344, 'duration': 5.123}, {'end': 202.03, 'text': "The visualization that I'm going to try is directly from that Numberphile video.", 'start': 198.707, 'duration': 3.323}, {'end': 204.632, 'text': 'And the rules for it were designed by Edmund Harris.', 'start': 202.07, 'duration': 2.562}, {'end': 209.215, 'text': "A link to the Numberphile video and more about Edmund Harris' work will be in this video's description.", 'start': 204.812, 'duration': 4.403}], 'summary': 'Visualizing the collatz conjecture with organic patterns inspired by a numberphile video.', 'duration': 45.288, 'max_score': 163.927, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/EYLWxwo1Ed8/pics/EYLWxwo1Ed8163927.jpg'}], 'start': 0.209, 'title': 'Collatz conjecture', 'summary': 'Explains the collatz conjecture, a sequence where any positive number reaches 1 through a specific process, with an example showing that starting at 5 takes 111 steps, and discusses visualizing the conjecture through a tree-like diagram inspired by a numberphile video.', 'chapters': [{'end': 140.439, 'start': 0.209, 'title': 'Coding the collatz conjecture', 'summary': 'Explains the collatz conjecture, a mathematical sequence where any positive number will eventually reach 1 through a specific calculation process, with an example showing that starting at 5 takes 111 steps, and provides resources for further exploration.', 'duration': 140.23, 'highlights': ['The Collatz Conjecture is a mathematical sequence where any positive number will eventually reach 1 through a specific calculation process, exemplified by starting at 5 taking 111 steps.', 'The chapter provides resources for further exploration, including links to different code examples and visualizations of the Collatz Conjecture.', 'The Collatz Conjecture was originally suggested as a topic on August 8, 2016, and the example of starting at 27 takes 111 steps is mentioned with a visualization of the value as it takes those steps.']}, {'end': 209.215, 'start': 140.439, 'title': 'Visualizing the kolatz conjecture', 'summary': 'Discusses visualizing the kolatz conjecture through a tree-like diagram, where specific numbers eventually converge to 1, and the visualization technique inspired by a numberphile video creates a seaweed-like pattern.', 'duration': 68.776, 'highlights': ['The visualization technique represents the Kolatz conjecture as a tree, illustrating how different numbers converge to 1, such as 25 becoming 76, 38, 19, and eventually 22.', 'The discussion explores the organic, seaweed-like pattern that emerges from the mathematical algorithm of the Kolatz conjecture visualization, inspired by the Numberphile video.', "The chapter mentions that the visualization technique is directly from a Numberphile video and the rules were designed by Edmund Harris, with a link to the video and more about Harris' work provided in the description."]}], 'duration': 209.006, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/EYLWxwo1Ed8/pics/EYLWxwo1Ed8209.jpg', 'highlights': ['The Collatz Conjecture is a mathematical sequence where any positive number will eventually reach 1 through a specific calculation process, exemplified by starting at 5 taking 111 steps.', 'The visualization technique represents the Kolatz conjecture as a tree, illustrating how different numbers converge to 1, such as 25 becoming 76, 38, 19, and eventually 22.', 'The discussion explores the organic, seaweed-like pattern that emerges from the mathematical algorithm of the Kolatz conjecture visualization, inspired by the Numberphile video.', 'The chapter provides resources for further exploration, including links to different code examples and visualizations of the Collatz Conjecture.', 'The Collatz Conjecture was originally suggested as a topic on August 8, 2016, and the example of starting at 27 takes 111 steps is mentioned with a visualization of the value as it takes those steps.']}, {'end': 562.058, 'segs': [{'end': 279.524, 'src': 'embed', 'start': 251.718, 'weight': 1, 'content': [{'end': 256.724, 'text': "I'm going to attempt to program this sequence in Processing, a Java-based creative coding environment.", 'start': 251.718, 'duration': 5.006}, {'end': 266.634, 'text': "One of the things I love about Processing is there's a library in Processing that allows you to render out a drawing to a PDF that you could blow up to large scale and print as a nice poster.", 'start': 257.004, 'duration': 9.63}, {'end': 270.258, 'text': "So maybe I'll make a nice, beautiful Collatz Conjecture coding train poster.", 'start': 266.655, 'duration': 3.603}, {'end': 274.841, 'text': "First thing I need is a function that's going to do the number sequence.", 'start': 271.058, 'duration': 3.783}, {'end': 276.482, 'text': "So let's just call that colots.", 'start': 275.061, 'duration': 1.421}, {'end': 279.524, 'text': "And it'll be a function that will receive any number.", 'start': 277.243, 'duration': 2.281}], 'summary': 'Using processing to create a large-scale pdf poster of collatz conjecture sequence.', 'duration': 27.806, 'max_score': 251.718, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/EYLWxwo1Ed8/pics/EYLWxwo1Ed8251718.jpg'}, {'end': 358.12, 'src': 'heatmap', 'start': 330.318, 'weight': 0.786, 'content': [{'end': 334.302, 'text': 'If I start with the number 10, I should get 5.', 'start': 330.318, 'duration': 3.984}, {'end': 341.067, 'text': "Now let's think about putting that into a loop, right? Let's see how long it takes for the number to get back to 1.", 'start': 334.302, 'duration': 6.765}, {'end': 345.291, 'text': 'This is like a weird scenario where maybe I might actually need to use a do while loop.', 'start': 341.067, 'duration': 4.224}, {'end': 353.076, 'text': 'Here is a do while loop.', 'start': 351.175, 'duration': 1.901}, {'end': 358.12, 'text': "I really think this might be the first time in my entire life that I've used a do while loop.", 'start': 353.096, 'duration': 5.024}], 'summary': 'Using a do while loop to transform 10 into 5 and back to 1 for the first time.', 'duration': 27.802, 'max_score': 330.318, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/EYLWxwo1Ed8/pics/EYLWxwo1Ed8330318.jpg'}, {'end': 444.304, 'src': 'embed', 'start': 387.239, 'weight': 0, 'content': [{'end': 388.355, 'text': '5, 16, 8, 4, 2, 1.', 'start': 387.239, 'duration': 1.116}, {'end': 391.682, 'text': 'Perfect So now we can test the Kolatz conjecture.', 'start': 388.36, 'duration': 3.322}, {'end': 394.904, 'text': "Let's say n equals 100.", 'start': 392.502, 'duration': 2.402}, {'end': 395.504, 'text': 'We got 1.', 'start': 394.904, 'duration': 0.6}, {'end': 398.305, 'text': 'n equals 1, 000.', 'start': 395.504, 'duration': 2.801}, {'end': 399.507, 'text': 'We got to 1.', 'start': 398.306, 'duration': 1.201}, {'end': 401.943, 'text': 'n equals 8, 3, 5, 2, 9, 1.', 'start': 399.507, 'duration': 2.436}, {'end': 405.01, 'text': 'Oh, I need my book of random numbers to try to start with a random number.', 'start': 401.948, 'duration': 3.062}, {'end': 408.07, 'text': 'We got to 1.', 'start': 406.65, 'duration': 1.42}, {'end': 413.171, 'text': 'Cool The Collatz conjecture seems to be true based on my simple processing code.', 'start': 408.07, 'duration': 5.101}, {'end': 417.692, 'text': "Let's just out of curiosity see the number of steps it takes.", 'start': 414.311, 'duration': 3.381}, {'end': 419.852, 'text': 'That equals 0.', 'start': 418.492, 'duration': 1.36}, {'end': 425.273, 'text': 'And then every time I call the Collatz function, steps goes up by 1.', 'start': 419.852, 'duration': 5.421}, {'end': 431.954, 'text': "Now, rather than print out the sequence, let's just print out the number of steps.", 'start': 425.273, 'duration': 6.681}, {'end': 434.115, 'text': '175 for that particular number.', 'start': 431.974, 'duration': 2.141}, {'end': 442.622, 'text': 'If I go back to the Wikipedia page, I can test to see if my code is performing correctly by picking.', 'start': 437.073, 'duration': 5.549}, {'end': 444.304, 'text': "let's just say, let's pick this number.", 'start': 442.622, 'duration': 1.682}], 'summary': 'Testing the collatz conjecture with various numbers, confirming its truth with simple processing code, and comparing results with the wikipedia page.', 'duration': 57.065, 'max_score': 387.239, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/EYLWxwo1Ed8/pics/EYLWxwo1Ed8387239.jpg'}, {'end': 502.062, 'src': 'embed', 'start': 470.18, 'weight': 4, 'content': [{'end': 472.301, 'text': "So I think I've gone probably way above that.", 'start': 470.18, 'duration': 2.121}, {'end': 481.045, 'text': 'So somewhere in the sequence, even though I started with a number around 670 million, I went way above the range probably of a 32-bit integer.', 'start': 472.741, 'duration': 8.304}, {'end': 485.088, 'text': 'So I think a way that I could probably fix this is by changing this to a long.', 'start': 481.225, 'duration': 3.863}, {'end': 490.433, 'text': 'A long is a data type in Java that also stores numbers but uses more memory than 32 bits.', 'start': 485.108, 'duration': 5.325}, {'end': 494.056, 'text': "I believe it's 64 bits, and I'll correct that if that's wrong somehow.", 'start': 490.533, 'duration': 3.523}, {'end': 502.062, 'text': 'So I need to change the function also to return a long and to accept a long.', 'start': 494.436, 'duration': 7.626}], 'summary': 'The number exceeded the range of a 32-bit integer, so it needs to be changed to a long data type in java.', 'duration': 31.882, 'max_score': 470.18, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/EYLWxwo1Ed8/pics/EYLWxwo1Ed8470180.jpg'}], 'start': 209.635, 'title': 'Visualization of collatz conjecture', 'summary': 'Discusses the programming and visualization of the collatz conjecture, including creating a large-scale poster using processing and the successful visualization of the collatz conjecture for numbers up to 10,000.', 'chapters': [{'end': 270.258, 'start': 209.635, 'title': 'Visualization of collatz conjecture', 'summary': 'Discusses the visualization and programming of the collatz conjecture, where starting with a number, the sequence involves dividing by 2 for even numbers and multiplying by 3 and adding 1 for odd numbers, to eventually create a large-scale poster using processing.', 'duration': 60.623, 'highlights': ['The Collatz Conjecture sequence involves dividing by 2 for even numbers and multiplying by 3 and adding 1 for odd numbers, creating a visualization of the sequence using a Java-based creative coding environment, and rendering it to a PDF for large-scale printing and poster creation in Processing.', 'Starting with the number 10, the sequence progresses to 5, then 16, demonstrating the application of the Collatz Conjecture.', 'The potential to create a large-scale poster using Processing and a library within Processing enhances the visualization of the Collatz Conjecture sequence.']}, {'end': 562.058, 'start': 271.058, 'title': 'Collatz conjecture visualization', 'summary': 'Discusses the creation of a function to test for even or odd numbers and then using it to validate the collatz conjecture, discovering that a 32-bit integer limit is surpassed, leading to the need to switch to using the long data type, resulting in a successful visualization of the collatz conjecture for numbers up to 10,000.', 'duration': 291, 'highlights': ["The Collatz function is created to test for even or odd numbers and to generate the next number in the sequence, with successful testing using numbers like 5 and 10. The function 'collatz' is designed to determine if a number is even or odd and to generate the next number in the sequence, successfully tested with numbers like 5 and 10.", 'The use of a do while loop to test the Collatz conjecture for various numbers, leading to the conclusion that the conjecture seems to hold true based on the simple processing code. A do while loop is utilized to test the Collatz conjecture for various numbers, leading to the conclusion that the conjecture seems to hold true based on the simple processing code.', 'The discovery of surpassing the 32-bit integer limit while testing the Collatz conjecture for larger numbers like 670 million, leading to the need to switch to using the long data type to successfully complete the visualization for numbers up to 10,000. Surpassing the 32-bit integer limit is discovered while testing the Collatz conjecture for larger numbers like 670 million, leading to the need to switch to using the long data type to successfully complete the visualization for numbers up to 10,000.', 'The successful completion of the visualization of the Collatz conjecture for numbers up to 10,000, allowing for the use of integers without encountering range limitations. The successful completion of the visualization of the Collatz conjecture for numbers up to 10,000, allowing for the use of integers without encountering range limitations.']}], 'duration': 352.423, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/EYLWxwo1Ed8/pics/EYLWxwo1Ed8209635.jpg', 'highlights': ['The successful completion of the visualization of the Collatz conjecture for numbers up to 10,000, allowing for the use of integers without encountering range limitations.', 'The potential to create a large-scale poster using Processing and a library within Processing enhances the visualization of the Collatz Conjecture sequence.', 'The use of a do while loop to test the Collatz conjecture for various numbers, leading to the conclusion that the conjecture seems to hold true based on the simple processing code.', 'The Collatz function is created to test for even or odd numbers and to generate the next number in the sequence, with successful testing using numbers like 5 and 10.', 'Surpassing the 32-bit integer limit is discovered while testing the Collatz conjecture for larger numbers like 670 million, leading to the need to switch to using the long data type to successfully complete the visualization for numbers up to 10,000.', 'Starting with the number 10, the sequence progresses to 5, then 16, demonstrating the application of the Collatz Conjecture.', 'The Collatz Conjecture sequence involves dividing by 2 for even numbers and multiplying by 3 and adding 1 for odd numbers, creating a visualization of the sequence using a Java-based creative coding environment, and rendering it to a PDF for large-scale printing and poster creation in Processing.']}, {'end': 855.686, 'segs': [{'end': 603.558, 'src': 'embed', 'start': 563.052, 'weight': 0, 'content': [{'end': 570.237, 'text': 'Finished So it actually did that incredibly quickly, running through the full Collatz conjecture algorithm for every single number from 1 to 10, 000.', 'start': 563.052, 'duration': 7.185}, {'end': 573.659, 'text': 'The computer can do that super quickly.', 'start': 570.237, 'duration': 3.422}, {'end': 575.36, 'text': "Let's see what happens if I start drawing.", 'start': 573.699, 'duration': 1.661}, {'end': 580.223, 'text': 'So I think an effective way for me to do this would be used to translate function.', 'start': 575.92, 'duration': 4.303}, {'end': 582.905, 'text': 'So the translate and rotate functions.', 'start': 580.484, 'duration': 2.421}, {'end': 592.711, 'text': 'So in processing, the translate function takes an x and a y and will move the origin point along a path according to that x and y value.', 'start': 583.385, 'duration': 9.326}, {'end': 598.335, 'text': 'So that x value, that y value, 0, 0 is translated to here potentially.', 'start': 592.972, 'duration': 5.363}, {'end': 603.558, 'text': "So let's say what I want to do is start the visualization at the bottom right here.", 'start': 598.615, 'duration': 4.943}], 'summary': 'Rapidly executed collatz algorithm for numbers 1 to 10,000; utilizing translate and rotate functions in processing for visualization.', 'duration': 40.506, 'max_score': 563.052, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/EYLWxwo1Ed8/pics/EYLWxwo1Ed8563052.jpg'}, {'end': 777.025, 'src': 'embed', 'start': 708.686, 'weight': 2, 'content': [{'end': 710.906, 'text': "I'm going to pick 30 degrees, somewhat arbitrarily.", 'start': 708.686, 'duration': 2.22}, {'end': 715.907, 'text': 'Or if pi is 108 degrees, this would be pi divided by 6.', 'start': 711.106, 'duration': 4.801}, {'end': 717.988, 'text': 'And I should also make this a variable.', 'start': 715.907, 'duration': 2.081}, {'end': 719.488, 'text': "So let's call this angle.", 'start': 718.248, 'duration': 1.24}, {'end': 721.348, 'text': "And let's say that's pi divided by 6.", 'start': 719.788, 'duration': 1.56}, {'end': 725.329, 'text': "So we're going to rotate by the angle in one direction.", 'start': 721.348, 'duration': 3.981}, {'end': 731.17, 'text': 'Otherwise, rotate by the angle in the negative direction.', 'start': 725.909, 'duration': 5.261}, {'end': 737.013, 'text': "For every number, I'm about to move along this path.", 'start': 731.93, 'duration': 5.083}, {'end': 738.974, 'text': "I want to check if it's even or odd.", 'start': 737.513, 'duration': 1.461}, {'end': 740.495, 'text': 'So I want to rotate this way or that way.', 'start': 739.014, 'duration': 1.481}, {'end': 742.816, 'text': 'And then I want to move in that direction.', 'start': 740.775, 'duration': 2.041}, {'end': 744.097, 'text': 'But I need to draw something.', 'start': 742.876, 'duration': 1.221}, {'end': 749.5, 'text': "So before I translate, let's say stroke 255.", 'start': 744.437, 'duration': 5.063}, {'end': 754.783, 'text': "And let's draw a line from wherever I am, 0, 0, to 0, common negative length.", 'start': 749.5, 'duration': 5.283}, {'end': 757.284, 'text': "And then I'm going to move to the end of this line.", 'start': 755.443, 'duration': 1.841}, {'end': 760.406, 'text': 'This is very similar to what I did in the fractal tree coding challenge.', 'start': 757.304, 'duration': 3.102}, {'end': 764.549, 'text': "So actually I think to test this out, I've got two things going on here.", 'start': 760.726, 'duration': 3.823}, {'end': 765.93, 'text': "I've got this like outer loop.", 'start': 764.569, 'duration': 1.361}, {'end': 768.793, 'text': 'I think I want to comment out the outer loop for a second.', 'start': 766.271, 'duration': 2.522}, {'end': 774.063, 'text': 'And I just want to test this idea out by starting with any given number.', 'start': 770.68, 'duration': 3.383}, {'end': 777.025, 'text': "So let's start with the number 500 and see what happens.", 'start': 774.343, 'duration': 2.682}], 'summary': 'Using programming, rotate and draw lines based on mathematical calculations and conditions.', 'duration': 68.339, 'max_score': 708.686, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/EYLWxwo1Ed8/pics/EYLWxwo1Ed8708686.jpg'}, {'end': 831.647, 'src': 'embed', 'start': 803.766, 'weight': 5, 'content': [{'end': 806.568, 'text': "When I come back to the next number, I'm going to be picking up from where it left off.", 'start': 803.766, 'duration': 2.802}, {'end': 815.513, 'text': 'So one way to deal with this is actually just call this function resetMatrix, which will reset everything just back to the original orientation.', 'start': 806.808, 'duration': 8.705}, {'end': 823.238, 'text': 'And then I can put that original translation right there, n equals i.', 'start': 815.854, 'duration': 7.384}, {'end': 825.239, 'text': 'This is taking a very long time.', 'start': 823.238, 'duration': 2.001}, {'end': 831.647, 'text': 'And I got the visualization hairball.', 'start': 828.885, 'duration': 2.762}], 'summary': 'Function resetmatrix resets orientation, n equals i, long processing time.', 'duration': 27.881, 'max_score': 803.766, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/EYLWxwo1Ed8/pics/EYLWxwo1Ed8803766.jpg'}], 'start': 563.052, 'title': 'Visualizing collatz conjecture and rotating numbers', 'summary': 'Covers visualizing the collatz conjecture algorithm using processing, demonstrating translate and rotate functions, and drawing/rotating numbers based on their even or odd status. it also discusses the process of converging numbers back to 1 and experimenting with starting numbers.', 'chapters': [{'end': 679.088, 'start': 563.052, 'title': 'Visualizing collatz conjecture in processing', 'summary': 'Discusses visualizing the collatz conjecture algorithm and utilizing translate and rotate functions in processing to create a visualization, with a demonstration of using vector math to move the origin point and the rotate function to shift the view of the canvas.', 'duration': 116.036, 'highlights': ['The chapter demonstrates running the full Collatz conjecture algorithm for every single number from 1 to 10,000 on a computer, highlighting its speed and efficiency.', 'The author explains the translate function in Processing, emphasizing its ability to move the origin point along a path according to specified x and y values, with a practical example of starting the visualization at a specific position on the canvas.', 'The author discusses using vector math to move slightly to the right or left by some angle, illustrating the use of sine and cosine to calculate the difference in x and y, and contrasts it with the functionality of the rotate function in shifting the view of the entire canvas for similar effects.']}, {'end': 757.284, 'start': 679.448, 'title': 'Drawing and rotating numbers', 'summary': 'Discusses rotating and drawing numbers by specific angles based on their even or odd status, with a focus on rotating by 30 degrees or pi/6 and drawing lines accordingly.', 'duration': 77.836, 'highlights': ['The chapter covers rotating and drawing numbers by specific angles based on their even or odd status, with a focus on rotating by 30 degrees or pi/6 and drawing lines accordingly.', 'The process involves checking if a number is even or odd and then rotating and drawing lines based on the result.', 'The chapter also mentions setting a stroke color of 255 and drawing lines from the current position to a specific point before moving to the end of the line.']}, {'end': 855.686, 'start': 757.304, 'title': 'Visualizing collatz conjecture', 'summary': 'Discusses the process of visualizing the collatz conjecture using coding, experimenting with starting numbers, and addressing errors encountered, aiming to converge all numbers back to 1.', 'duration': 98.382, 'highlights': ['Experimenting with starting numbers, such as 500, and observing the results.', 'Addressing the issue of all numbers starting back at the same place to enable visualization.', 'Implementing the resetMatrix function to reset everything back to the original orientation for each iteration.', 'Recognizing errors in the visualization process and acknowledging misconceptions about the Collatz Conjecture.']}], 'duration': 292.634, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/EYLWxwo1Ed8/pics/EYLWxwo1Ed8563052.jpg', 'highlights': ['The chapter demonstrates running the full Collatz conjecture algorithm for every single number from 1 to 10,000 on a computer, highlighting its speed and efficiency.', 'The author explains the translate function in Processing, emphasizing its ability to move the origin point along a path according to specified x and y values, with a practical example of starting the visualization at a specific position on the canvas.', 'The chapter covers rotating and drawing numbers by specific angles based on their even or odd status, with a focus on rotating by 30 degrees or pi/6 and drawing lines accordingly.', 'The process involves checking if a number is even or odd and then rotating and drawing lines based on the result.', 'Experimenting with starting numbers, such as 500, and observing the results.', 'Implementing the resetMatrix function to reset everything back to the original orientation for each iteration.']}, {'end': 1073.965, 'segs': [{'end': 900.269, 'src': 'embed', 'start': 874.851, 'weight': 0, 'content': [{'end': 880.595, 'text': "A float list in processing, and I'm going to call that sequence, is just a sequence of numbers.", 'start': 874.851, 'duration': 5.744}, {'end': 883.557, 'text': 'And I could just use a plain array or an array list.', 'start': 881.096, 'duration': 2.461}, {'end': 888.641, 'text': 'But a float list is nice because it just works really easily with floating point numbers.', 'start': 883.617, 'duration': 5.024}, {'end': 890.082, 'text': "And it's completely resizable.", 'start': 888.861, 'duration': 1.221}, {'end': 890.782, 'text': 'And I can iterate.', 'start': 890.122, 'duration': 0.66}, {'end': 891.463, 'text': 'I can reverse it.', 'start': 890.822, 'duration': 0.641}, {'end': 892.503, 'text': 'I can do all sorts of things.', 'start': 891.503, 'duration': 1}, {'end': 894.665, 'text': 'So I want to create a float list.', 'start': 893.044, 'duration': 1.621}, {'end': 897.987, 'text': "And I'm going to take all of this drawing stuff out.", 'start': 895.325, 'duration': 2.662}, {'end': 900.269, 'text': "Let's just put it down here, comment it.", 'start': 898.328, 'duration': 1.941}], 'summary': 'Processing float list is resizable and works well with floating point numbers, allowing various operations.', 'duration': 25.418, 'max_score': 874.851, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/EYLWxwo1Ed8/pics/EYLWxwo1Ed8874851.jpg'}, {'end': 950.386, 'src': 'embed', 'start': 920.046, 'weight': 1, 'content': [{'end': 921.106, 'text': "I don't know why I said float list.", 'start': 920.046, 'duration': 1.06}, {'end': 922.227, 'text': "It's just integers.", 'start': 921.366, 'duration': 0.861}, {'end': 924.868, 'text': 'So it could only be integers in the co-op sequence.', 'start': 922.247, 'duration': 2.621}, {'end': 929.718, 'text': 'Now I can visualize the list.', 'start': 926.036, 'duration': 3.682}, {'end': 935.72, 'text': 'I want to visualize the list from the end all the way up to the beginning.', 'start': 930.198, 'duration': 5.522}, {'end': 941.803, 'text': 'Sequence.reverse And then iterate through the entire list.', 'start': 936.06, 'duration': 5.743}, {'end': 945.865, 'text': 'Int j equals 0.', 'start': 942.423, 'duration': 3.442}, {'end': 950.386, 'text': 'j is less than sequence.size j++.', 'start': 945.865, 'duration': 4.521}], 'summary': 'Visualizing a sequence of integers in reverse order.', 'duration': 30.34, 'max_score': 920.046, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/EYLWxwo1Ed8/pics/EYLWxwo1Ed8920046.jpg'}, {'end': 1047.413, 'src': 'embed', 'start': 1018.06, 'weight': 2, 'content': [{'end': 1020.905, 'text': "So I'm going to try different numbers to sort of get the feeling of it.", 'start': 1018.06, 'duration': 2.845}, {'end': 1024.691, 'text': "Let's try pi divided by 12.", 'start': 1021.305, 'duration': 3.386}, {'end': 1026.534, 'text': "So I'm going to have that.", 'start': 1024.691, 'duration': 1.843}, {'end': 1030.566, 'text': "Yeah, I think it's probably a very small amount.", 'start': 1027.185, 'duration': 3.381}, {'end': 1034.928, 'text': "So we can see that's what's happening with the number 100.", 'start': 1030.945, 'duration': 3.983}, {'end': 1038.169, 'text': 'I also might want to think about which way am I going.', 'start': 1034.928, 'duration': 3.241}, {'end': 1041.01, 'text': "It's kind of going to orient this whole pattern.", 'start': 1038.189, 'duration': 2.821}, {'end': 1047.413, 'text': "And maybe actually I'm starting in a direction that's not straight.", 'start': 1041.39, 'duration': 6.023}], 'summary': 'Exploring mathematical patterns with different numbers and orientations.', 'duration': 29.353, 'max_score': 1018.06, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/EYLWxwo1Ed8/pics/EYLWxwo1Ed81018060.jpg'}], 'start': 857.267, 'title': 'Creating and visualizing number sequences in processing', 'summary': 'Explains creating sequences using float and integer lists in processing, emphasizing easy manipulation, resizing, iterating, reversing, and visualizing the lists, and exploring number patterns using rotation, including testing with values such as pi/12 and 100, and observing results with numbers from 1 to 10,000 while encountering technical difficulties.', 'chapters': [{'end': 919.946, 'start': 857.267, 'title': 'Creating a sequence with float list in processing', 'summary': 'Explains the process of creating a sequence using a float list in processing, which provides easy manipulation of floating point numbers and is completely resizable.', 'duration': 62.679, 'highlights': ['Creating a float list in Processing, called sequence, for easily manipulating and resizing a sequence of numbers.', 'Using a float list to append every single value of n and then adding 1 to it at the end.']}, {'end': 979.187, 'start': 920.046, 'title': 'Iterating and reversing integer list', 'summary': 'Discusses iterating through an integer list, reversing the sequence, and visualizing the list, emphasizing the process of reversing and iterating through the list from the end to the beginning.', 'duration': 59.141, 'highlights': ["The process involves visualizing and iterating through the integer list from the end to the beginning, emphasizing the use of 'Sequence.reverse' and 'j++' to iterate through the entire list.", 'The speaker considers potential naming conflicts and rethinks the naming convention for the variables in the code.', "The chapter briefly mentions the initial confusion about using 'float list' instead of 'integers' in the cooperative sequence."]}, {'end': 1073.965, 'start': 979.707, 'title': 'Exploring number patterns with rotation', 'summary': 'Explores creating patterns based on numbers with rotation, testing with various values such as pi divided by 12 and 100, and eventually observing the results with numbers from 1 to 10,000, while also encountering technical difficulties.', 'duration': 94.258, 'highlights': ['The chapter explores creating patterns based on numbers with rotation, testing with various values such as pi divided by 12 and 100, and eventually observing the results with numbers from 1 to 10,000, while also encountering technical difficulties.', 'The speaker experimented with different numbers, such as pi divided by 12, to observe the resulting patterns.', 'The speaker encountered technical difficulties during the process, including a camera dying and a memory card filling up.']}], 'duration': 216.698, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/EYLWxwo1Ed8/pics/EYLWxwo1Ed8857267.jpg', 'highlights': ['Creating a float list in Processing, called sequence, for easily manipulating and resizing a sequence of numbers.', "The process involves visualizing and iterating through the integer list from the end to the beginning, emphasizing the use of 'Sequence.reverse' and 'j++' to iterate through the entire list.", 'The chapter explores creating patterns based on numbers with rotation, testing with various values such as pi divided by 12 and 100, and eventually observing the results with numbers from 1 to 10,000, while also encountering technical difficulties.']}, {'end': 1376.456, 'segs': [{'end': 1119.884, 'src': 'embed', 'start': 1093.656, 'weight': 0, 'content': [{'end': 1104.7, 'text': 'Any time I apply the algorithm for when I have an odd number, 3n plus 1, that is always going to result in an even number.', 'start': 1093.656, 'duration': 11.044}, {'end': 1107.421, 'text': "So what's the next step? Divide by 2.", 'start': 1105, 'duration': 2.421}, {'end': 1113.062, 'text': 'So I could actually, in the Collatz conjecture code, sort of speed up the process of getting to 1.', 'start': 1107.421, 'duration': 5.641}, {'end': 1119.884, 'text': "It's not going to compute the exact number of steps, but it could speed up the process of getting to 1 by just taking this down here.", 'start': 1113.062, 'duration': 6.822}], 'summary': 'Applying the 3n plus 1 algorithm results in even numbers, followed by dividing by 2 to speed up the process of reaching 1.', 'duration': 26.228, 'max_score': 1093.656, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/EYLWxwo1Ed8/pics/EYLWxwo1Ed81093656.jpg'}, {'end': 1162.756, 'src': 'embed', 'start': 1137.113, 'weight': 2, 'content': [{'end': 1144.379, 'text': "I can get something that's quite a bit more control and in a way more closer to what the result in that number file video is.", 'start': 1137.113, 'duration': 7.266}, {'end': 1147.001, 'text': "So I think there's a bit more that I can do with this.", 'start': 1144.399, 'duration': 2.602}, {'end': 1154.527, 'text': 'Number one is let me instead of moving up, let me give myself more space to work with and move in a horizontal direction.', 'start': 1147.382, 'duration': 7.145}, {'end': 1160.973, 'text': "So I'm actually going to start at 0.", 'start': 1155.088, 'duration': 5.885}, {'end': 1162.756, 'text': 'height divided by 2.', 'start': 1160.973, 'duration': 1.783}], 'summary': 'Exploring greater control and precision in a horizontal direction, starting at 0 and height divided by 2.', 'duration': 25.643, 'max_score': 1137.113, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/EYLWxwo1Ed8/pics/EYLWxwo1Ed81137113.jpg'}, {'end': 1228.592, 'src': 'embed', 'start': 1195.93, 'weight': 3, 'content': [{'end': 1196.33, 'text': 'Look at this.', 'start': 1195.93, 'duration': 0.4}, {'end': 1198.051, 'text': 'Interesting Huh.', 'start': 1196.47, 'duration': 1.581}, {'end': 1204.915, 'text': "The other thing about what's going on here is since everything converges to 1, ultimately there's a lot of repeating patterns.", 'start': 1198.432, 'duration': 6.483}, {'end': 1213.881, 'text': 'So I think this could have a more organic-like feel if I start to give the line some alpha so that the repeating patterns become much brighter.', 'start': 1205.576, 'duration': 8.305}, {'end': 1216.923, 'text': 'And as it branches out, it sort of fades away.', 'start': 1214.061, 'duration': 2.862}, {'end': 1220.365, 'text': 'So let me just give everything an alpha of 50.', 'start': 1217.283, 'duration': 3.082}, {'end': 1228.592, 'text': 'What happens if I make that angle really, really small? Maybe I should stop dividing by pi and just do something like 0.0, 0.02.', 'start': 1220.365, 'duration': 8.227}], 'summary': 'Discussion on creating organic-like patterns with repeating elements and adjusting alpha and angle values.', 'duration': 32.662, 'max_score': 1195.93, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/EYLWxwo1Ed8/pics/EYLWxwo1Ed81195930.jpg'}, {'end': 1287.528, 'src': 'embed', 'start': 1245.528, 'weight': 1, 'content': [{'end': 1252.454, 'text': 'Just take a minute to ponder the fact that this very formal, mathematical,', 'start': 1245.528, 'duration': 6.926}, {'end': 1263.357, 'text': 'highly repetitious pattern can somehow be turned into this feeling of seaweed, of growth, of organic nature,', 'start': 1252.454, 'duration': 10.903}, {'end': 1265.577, 'text': 'like the plants that are right outside this window.', 'start': 1263.357, 'duration': 2.22}, {'end': 1270.098, 'text': 'What kind of beauty can you make out of this algorithm? I would love to see.', 'start': 1266.097, 'duration': 4.001}, {'end': 1272.099, 'text': 'Let me show you one more thing very quickly.', 'start': 1270.118, 'duration': 1.981}, {'end': 1277.16, 'text': 'Let me have this render to a PDF so I could blow it up and make it a very big poster if I wanted to.', 'start': 1272.419, 'duration': 4.741}, {'end': 1278.08, 'text': 'Let me show you how to do that.', 'start': 1277.18, 'duration': 0.9}, {'end': 1281.803, 'text': "So I'm here on the PDF export page on the processing website.", 'start': 1278.82, 'duration': 2.983}, {'end': 1283.464, 'text': "And there's a bunch of different ways to do it.", 'start': 1282.003, 'duration': 1.461}, {'end': 1286.167, 'text': 'This is actually what I want to do here, single frame.', 'start': 1283.865, 'duration': 2.302}, {'end': 1287.528, 'text': 'Actually, I want to see it on screen.', 'start': 1286.207, 'duration': 1.321}], 'summary': 'Transforming a formal pattern into organic nature; showcasing pdf export process.', 'duration': 42, 'max_score': 1245.528, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/EYLWxwo1Ed8/pics/EYLWxwo1Ed81245528.jpg'}, {'end': 1376.456, 'src': 'heatmap', 'start': 1331.208, 'weight': 6, 'content': [{'end': 1332.909, 'text': "It's taking a while for it to load.", 'start': 1331.208, 'duration': 1.701}, {'end': 1336.752, 'text': "But what's nice about this, it's vector graphics.", 'start': 1333.109, 'duration': 3.643}, {'end': 1341.215, 'text': 'So you can see my machine and the Mac Preview app is having taken a while to render.', 'start': 1336.772, 'duration': 4.443}, {'end': 1345.579, 'text': "But I can blow this up very, very large, and it won't be pixelated.", 'start': 1341.456, 'duration': 4.123}, {'end': 1347.42, 'text': 'So make a version of this.', 'start': 1345.919, 'duration': 1.501}, {'end': 1350.443, 'text': 'Make a PDF, a vector file of it.', 'start': 1347.721, 'duration': 2.722}, {'end': 1351.224, 'text': 'Print it.', 'start': 1350.743, 'duration': 0.481}, {'end': 1357.789, 'text': "I'm going to hang one of these up back here or in my office somewhere or in the studio at NYU or here in the cabana.", 'start': 1351.384, 'duration': 6.405}, {'end': 1362.133, 'text': 'Who knows? Thank you for watching this second episode of Coding in the Cabana.', 'start': 1357.849, 'duration': 4.284}, {'end': 1364.015, 'text': "I'm going to go water the plants.", 'start': 1363.054, 'duration': 0.961}, {'end': 1376.376, 'text': 'Alright, thanks so much for spending your time with me and I hope to see you next time on Coding in the Cabana.', 'start': 1370.976, 'duration': 5.4}, {'end': 1376.456, 'text': 'Bye!.', 'start': 1376.396, 'duration': 0.06}], 'summary': 'Vector graphics ensures high-quality, scalable output for printing and display.', 'duration': 43.347, 'max_score': 1331.208, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/EYLWxwo1Ed8/pics/EYLWxwo1Ed81331208.jpg'}], 'start': 1074.485, 'title': 'Optimizing collatz conjecture visualization, algorithmic art, and rendering pdf from processing website', 'summary': 'Discusses optimizing the collatz conjecture visualization for a more controlled and closer result, explores transforming mathematical patterns into organic-like art, and demonstrates rendering pdfs using the processing library for large-scale printing.', 'chapters': [{'end': 1193.334, 'start': 1074.485, 'title': 'Optimizing collatz conjecture visualization', 'summary': 'Discusses optimizing the collatz conjecture visualization by applying the algorithm to speed up the process of reaching 1, resulting in a more controlled and closer result to the number file video, and making adjustments to the visualization to have more space and move in a horizontal direction.', 'duration': 118.849, 'highlights': ['Applying algorithm to speed up the process of reaching 1 By applying the algorithm for odd numbers (3n+1) and dividing by 2, the process of reaching 1 can be sped up, though not computing the exact number of steps.', 'Adjusting visualization for more control and space Making adjustments to the visualization to have more space to work with, move in a horizontal direction, and translate along the x-axis for a more controlled result.']}, {'end': 1272.099, 'start': 1195.93, 'title': 'Algorithmic art and organic patterns', 'summary': 'Explores the process of transforming repetitious mathematical patterns into organic-like art, pondering the beauty and potential of the algorithm, and experimenting with alpha and angle adjustments to achieve a more natural feel.', 'duration': 76.169, 'highlights': ['By adjusting the alpha of the lines and branching out, the repeating patterns can be transformed into a more organic-like feel, potentially creating brighter and fading patterns (quantifiable data: alpha of 50).', 'Experimenting with different angles and small divisions, the author attempts to achieve a similar, organic look, acknowledging the resemblance to seaweed and organic growth (quantifiable data: angle adjustments, division by 0.02).', 'The author reflects on the transformation of a formal, repetitious mathematical pattern into the feeling of seaweed and organic nature, highlighting the potential beauty that can be derived from the algorithm (quantifiable data: reflection on the transformation).']}, {'end': 1376.456, 'start': 1272.419, 'title': 'Rendering pdf from processing website', 'summary': 'Demonstrates how to render a pdf using the processing library, enabling the creation of vector graphics for large-scale printing, with a mention of potential usage locations and a sign-off for the episode.', 'duration': 104.037, 'highlights': ['Rendering PDF with vector graphics for large-scale printing The speaker discusses rendering the PDF using the processing library, emphasizing the ability to create vector graphics suitable for large-scale printing.', 'Mention of potential usage locations for the printed PDF The speaker mentions potential locations for using the printed PDF, including the cabana, office, and studio at NYU.', 'Sign-off for the episode The speaker concludes by thanking the audience and expressing the hope to see them in the next episode of Coding in the Cabana.']}], 'duration': 301.971, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/EYLWxwo1Ed8/pics/EYLWxwo1Ed81074485.jpg', 'highlights': ['Applying algorithm to speed up the process of reaching 1 By applying the algorithm for odd numbers (3n+1) and dividing by 2, the process of reaching 1 can be sped up, though not computing the exact number of steps.', 'Rendering PDF with vector graphics for large-scale printing The speaker discusses rendering the PDF using the processing library, emphasizing the ability to create vector graphics suitable for large-scale printing.', 'Adjusting visualization for more control and space Making adjustments to the visualization to have more space to work with, move in a horizontal direction, and translate along the x-axis for a more controlled result.', 'By adjusting the alpha of the lines and branching out, the repeating patterns can be transformed into a more organic-like feel, potentially creating brighter and fading patterns (quantifiable data: alpha of 50).', 'Experimenting with different angles and small divisions, the author attempts to achieve a similar, organic look, acknowledging the resemblance to seaweed and organic growth (quantifiable data: angle adjustments, division by 0.02).', 'The author reflects on the transformation of a formal, repetitious mathematical pattern into the feeling of seaweed and organic nature, highlighting the potential beauty that can be derived from the algorithm (quantifiable data: reflection on the transformation).', 'Mention of potential usage locations for the printed PDF The speaker mentions potential locations for using the printed PDF, including the cabana, office, and studio at NYU.', 'Sign-off for the episode The speaker concludes by thanking the audience and expressing the hope to see them in the next episode of Coding in the Cabana.']}], 'highlights': ['The visualization technique represents the Kolatz conjecture as a tree, illustrating how different numbers converge to 1, such as 25 becoming 76, 38, 19, and eventually 22.', 'The successful completion of the visualization of the Collatz conjecture for numbers up to 10,000, allowing for the use of integers without encountering range limitations.', 'The chapter demonstrates running the full Collatz conjecture algorithm for every single number from 1 to 10,000 on a computer, highlighting its speed and efficiency.', 'Creating a float list in Processing, called sequence, for easily manipulating and resizing a sequence of numbers.', 'Applying algorithm to speed up the process of reaching 1 By applying the algorithm for odd numbers (3n+1) and dividing by 2, the process of reaching 1 can be sped up, though not computing the exact number of steps.', 'Rendering PDF with vector graphics for large-scale printing The speaker discusses rendering the PDF using the processing library, emphasizing the ability to create vector graphics suitable for large-scale printing.', 'Adjusting visualization for more control and space Making adjustments to the visualization to have more space to work with, move in a horizontal direction, and translate along the x-axis for a more controlled result.', 'By adjusting the alpha of the lines and branching out, the repeating patterns can be transformed into a more organic-like feel, potentially creating brighter and fading patterns (quantifiable data: alpha of 50).', 'Experimenting with different angles and small divisions, the author attempts to achieve a similar, organic look, acknowledging the resemblance to seaweed and organic growth (quantifiable data: angle adjustments, division by 0.02).', 'The author reflects on the transformation of a formal, repetitious mathematical pattern into the feeling of seaweed and organic nature, highlighting the potential beauty that can be derived from the algorithm (quantifiable data: reflection on the transformation).']}