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A tribute to #Numberphile and their video on the Recamán Sequence: 🤍 Check out their video to see what the numbers mean. When visualized as loops and circles, the Recamán Sequence starts as an interesting swirly pattern, but when you extend it to more and more terms, a clear fractal structure begins to emerge. I believe this is the largest animation of the sequence yet created, with 300,000 terms. For this version, I highlighted the fractal pattern in different colors to make it clearer, and I also made the animation speed up exponentially so it doesn't get bogged down on the large numbers. Music: Anitra's Dance (abridged) and In the Hall of the Mountain King from Peer Gynt by Edvard Grieg. Public domain recording courtesy of the Musopen Symphony.
Check out Brilliant (and get 20% off their premium service): 🤍 (sponsor)... More links & stuff in full description below ↓↓↓ Check out Brilliant's Problem of the Week (it's free): 🤍 Alex Bellos: 🤍 The coloring book featuring the Recamán Sequence: 🤍 More videos with Alex: 🤍 The Recamán Sequence on the OEIS: 🤍 Full length video of Tiffany Arment coloring the patern: 🤍 Tiffany Arment: 🤍 Thanks also to Edmund Harriss. Patreon: 🤍 Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): 🤍 We are also supported by Science Sandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science. 🤍 And support from Math For America - 🤍 NUMBERPHILE Website: 🤍 Numberphile on Facebook: 🤍 Numberphile tweets: 🤍 Subscribe: 🤍 Videos by Brady Haran Numberphile T-Shirts: 🤍 Brady's videos subreddit: 🤍 Brady's latest videos across all channels: 🤍 Sign up for (occasional) emails: 🤍
The Recaman Sequence is described here: 🤍 One can map the items in this sequence to the frequencies of various notes in different scales (chromatic, major, minor, pentatonic, major/minor blues, etc...) to generate audio files and create music. Code here (See vid11): 🤍
In this coding challenge, I visualize the Recamán’s number sequence using the p5.js library and go on to generate a series of musical tones using p5.js sound. Code: 🤍 p5.js Web Editor Sketches: 🕹️ Recamán's Sequence - Part 1: 🤍 🕹️ Recamán's Sequence - Part 2: 🤍 Other Parts of this Challenge: 📺 Recamán's Sequence - Part 2: 🤍 🎥 Previous video: 🤍 🎥 Next video: 🤍 🎥 All videos: 🤍 References: 📘 Recamán's Sequence on MathWorld: 🤍 🔖 Recamán's Sequence on Wikipedia: 🤍 🗐 OEIS: 🤍 🗏 Bernardo Recamán Santos: 🤍 Videos: 👻 The Slightly Spooky Recamán's Sequence: 🤍 🎹 Recamán's Sequence by Dale Gerdemann: 🤍 🚂 Tutorial Playlist on p5.js Sound: 🤍 🔴 Coding Train Live 146: 🤍 Related Coding Challenges: 🚂 #140 Leibniz Formula for Pi: 🤍 🚂 #133 Times Tables Cardioid Visualization: 🤍 🚂 #C2 Collatz Conjecture: 🤍 Timestamps: 0:00 Introduction! 1:56 Discussing the Recamán's Sequence 6:08 Starting to code and adding the prerequisites to generate the sequence 7:18 Writing the algorithm to generate the numbers of the sequence 8:36 Testing the algorithm 9:40 Adding the counter 10:44 Visualizing the algorithm! 13:48 Making continuous series of arcs instead of ellipses 16:20 An exercise to pause and try for yourself! 16:50 Creating an Arc class and an array of arcs 19:33 Scaling down the animation as we move along the Recamán's Sequence 21:34 Scaling down by the biggest number in the sequence generated so far 22:34 Explore the Recamán's Sequence and share your works! Editing by Mathieu Blanchette Animations by Jason Heglund Music from Epidemic Sound 🚂 Website: 🤍 👾 Share Your Creation! 🤍 🚩 Suggest Topics: 🤍 💡 GitHub: 🤍 💬 Discord: 🤍 💖 Membership: 🤍 🛒 Store: 🤍 🖋️ Twitter: 🤍 📸 Instagram: 🤍 🎥 Coding Challenges: 🤍 🎥 Intro to Programming: 🤍 🔗 p5.js: 🤍 🔗 p5.js Web Editor: 🤍 🔗 Processing: 🤍 📄 Code of Conduct: 🤍 This description was auto-generated. If you see a problem, please open an issue: 🤍 #numbersequence #recamanssequence #music #audiovisual #visualization #p5js #javascript
In this coding challenge, I visualize the Recamán’s number sequence using the p5.js library and go on to generate a series of musical tones using p5.js sound. Code: 🤍 p5.js Web Editor Sketches: 🕹️ Recamán's Sequence - Part 1: 🤍 🕹️ Recamán's Sequence - Part 2: 🤍 Other Parts of this Challenge: 📺 Recamán's Sequence - Part 1: 🤍 🎥 Previous video: 🤍 🎥 Next video: 🤍 🎥 All videos: 🤍 References: 📘 Recamán's Sequence on MathWorld: 🤍 🔖 Recamán's Sequence on Wikipedia: 🤍 🗐 OEIS: 🤍 🗏 Bernardo Recamán Santos: 🤍 Videos: 👻 The Slightly Spooky Recamán's Sequence: 🤍 🎹 Recamán's Sequence by Dale Gerdemann: 🤍 🚂 Tutorial Playlist on p5.js Sound: 🤍 🔴 Coding Train Live 146: 🤍 Related Coding Challenges: 🚂 #140 Leibniz Formula for Pi: 🤍 🚂 #133 Times Tables Cardioid Visualization: 🤍 🚂 #C2 Collatz Conjecture: 🤍 Timestamps: 0:00 Welcome to the second part of the challenge! 2:19 Creating an oscillator using the p5.js sound library 4:00 Using the numbers of the Recamán's Sequence as the frequency of the oscillator 5:25 Thinking of the numbers of the sequence as keys of a piano! 7:54 Creating an envelope using the p5.js sound library 10:52 Restricting the frequency range 14:05 Conclusion! Editing by Mathieu Blanchette Animations by Jason Heglund Music from Epidemic Sound 🚂 Website: 🤍 👾 Share Your Creation! 🤍 🚩 Suggest Topics: 🤍 💡 GitHub: 🤍 💬 Discord: 🤍 💖 Membership: 🤍 🛒 Store: 🤍 🖋️ Twitter: 🤍 📸 Instagram: 🤍 🎥 Coding Challenges: 🤍 🎥 Intro to Programming: 🤍 🔗 p5.js: 🤍 🔗 p5.js Web Editor: 🤍 🔗 Processing: 🤍 📄 Code of Conduct: 🤍 This description was auto-generated. If you see a problem, please open an issue: 🤍 #numbersequence #recamanssequence #music #audiovisual #visualization #p5js #javascript
Visualizing a rather stunning number sequence , called the Recamán sequence in VEX. Support us on Patreon: 🤍 Watch Numberphile's video about Recamán's sequence here: 🤍 Download Project File (.hip): 🤍
Neil Sloane from the OEIS has another number sequence which escalates quickly. More links & stuff in full description below ↓↓↓ More videos with Neil Sloane: 🤍 Levine's sequence on the OEIS: 🤍 Neil is the founder and keeper of the The On-Line Encyclopedia of Integer Sequences: 🤍 Numberphile Podcast: 🤍 Unmade Podcast: 🤍 Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): 🤍 We are also supported by Science Sandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science. 🤍 And support from Math For America - 🤍 NUMBERPHILE Website: 🤍 Numberphile on Facebook: 🤍 Numberphile tweets: 🤍 Subscribe: 🤍 Videos by Brady Haran Patreon: 🤍 Numberphile T-Shirts and Merch: 🤍 Brady's videos subreddit: 🤍 Brady's latest videos across all channels: 🤍 Sign up for (occasional) emails: 🤍
For an explanation of this sequence, see the Numberphile video on it 🤍 I used alternating arcs, 4x anti-aliasing and 20 iterations per second. Took about 2 days to render on my laptop. "Ieder rondje is anders"
A Direct2D (and some C AMP) visualization of the mysterious Recamán sequence.
Simple program to generate and visualize the Recaman's Sequence, made in C using DevCpp. Information about the Recaman's Sequence 🤍 Numberphile 🤍 code (🤍 exe (🤍 Music Track : I Need to Start Writing Things Down - Chris Zabriskie
Please don't forget to subscribe. Recamán sequence piano song from The Online Encyclopedia of Integer Sequences. 🤍
A video illustrating the Recamán sequence OEIS A005132. We use an arc above the line to join successive terms if the latter term is even, and below if odd. The most current curve appears in violet, with the rest of the spectrum remapping across all previous curves as n increases. Tempo is 6 beats per second. The music that accompanies this illustration is generated by the sequence. The tones of piano keys are offset from middle C by k halftones, where k = [a(n) mod 64] − 24. a(n) greater than 2 a(n − 1) are accompanied by timpani out of phase with the increment. Record-setting a(n) are accentuated by splash cymbal. Runs greater than 1 of successive ascending or descending a(n) trigger a hi hat. Declining a(n) are accompanied by bass drum, sounds like a heartbeat. Enjoy!
he Recamán's sequence[1][2] (or Recaman's sequence) is a well known sequence defined by a recurrence relation, because its elements are related to the previous elements in a straightforward way, they are often defined using recursion.
Full article here: 🤍 Vojta Maur: 🤍 🤍
Main video is at: 🤍 Coloring by Tiffany Arment: 🤍 NUMBERPHILE Website: 🤍 Numberphile on Facebook: 🤍 Numberphile tweets: 🤍 Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): 🤍 Videos by Brady Haran Support us on Patreon: 🤍 Brady's videos subreddit: 🤍 A run-down of Brady's channels: 🤍 Sign up for (occasional) emails: 🤍
Simon has created the Recaman Sequence audio in Wolfram! First with 70 notes, then with 300 notes. See the code here: 🤍 Simon has been completely carried away by Wolfram Mathematica. He keeps starting new projects, just to try something out. After working on his Knot Theory book for days, and making beautiful illustrations in Wolfram, he switched over to domain coloring. The images below are some impressions of his experimenting with the color function. He hasn’t applied the complex function yet. Another new project he started has been Poisson disc sampling. “Wolfram is the most advanced language! It has most built-in stuff in it! At Wolfram, they are working so hard, that the knowledge base is changing every second!” Simon screams out as he pauses the Elementary Introduction to Wolfram Language book (he was reading it at first and now binge watches it as a series of video tutorials). Simon has been especially blown away by the free-form linguistic input: “From plane English it somehow computes the results and maybe even native Mathematica Syntax!” Wolfram also “has an entire section which is machine learning!”
For an explanation of this sequence, see the Numberphile video on it 🤍 To keep the lines visible, I applied a Gaussian filter and some sharpening. Took about 8 hours to render on my laptop.
Exploring Recamán's Sequence in p5.js + starting to explore the ml5.js library. 35:37 - Recamán's Sequence 1:27:05 - Sound Experiments with Recamán's Sequence 2:28:25 - ml5 Image Classifier 🔗 Recamán's Sequence on MathWorld: 🤍 🔗 TensorFlow.js: 🤍 🔗 ml5.js: 🤍 🔗 Nature of Code: 🤍 🔗 OEIS: 🤍 🔗 Bernardo Recamán Santos on Wikipedia: 🤍 🔗 ml5 on Adjacent: 🤍 🔗 MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications: 🤍 🎥 Recamán's Sequence by Numberphile: 🤍 🎥 TensorFlow.js Color Classifier: 🤍 🎥 TensorFlow.js playlist: 🤍 🎥 pcomp on Vimeo: 🤍 🎥 ADSR Envelope with p5.js: 🤍 🎥 Sound Synthesis with p5.js: 🤍 🚂 Website: 🤍 💖 Patreon: 🤍 🛒 Store: 🤍 📚 Book recommendations: 🤍 💻 🤍 🎥 For an Introduction to Programming: 🤍 🎥 To watch archived Live Streams: 🤍 🎥 For more Coding Challenges: 🤍 🔗 🤍 🔗 🤍 📄 Code of Conduct: 🤍
The Recaman sequence (A005132 at OEIS) was made famous as the background music for the OEIS Movie. It sounds rather different here since it is played using A003714 Fibbinary (or Zeckendorf base). Playing in fibbinary base means that each element of the sequence is mapped to a Fibbinary numerical representation and then each '1' from this form is mapped to a note. One feature of fibbinary is that the digits tend to be maximally separated. This tends to make the chords sound good without me having to know anything about music theory. An earlier version of this video used phinary instead of fibbinary. The suggestion to switch to Fibbinary came from Robert Munafo, who also suggested that I adjust the volume so that notes with higher pitch, corresponding to more significant digits, should be played louder. I adopted this suggestion as well, but then added soloists so that at least some of the time you can hear what is happening with the less significant digits. I have offered to start an open source project to make OEIS-related videos such as this using Java. Let me know if you are interested in participating.
This is a visualization of Recamán Sequence. It looks fairly cool. Based on this Numberphile video: 🤍 Made in Processing 3. Here's the code. Note that it's incredibly slow (This took 40 minutes to record). 🤍
There's a great Numberphile video on this sequence, and I decided to make the visuals in the video myself: 🤍 See my channel description for general information on my videos.
Neil Sloane speaks at the Experimental Mathematics Seminar. Abstract: A half-dozen lovely new sequences from the On-Line Encyclopedia of Integer Sequences, with brilliant illustrations and many open problems.
Thanks Squarespace: 🤍 More links & stuff in full description below ↓↓↓ Full length colouring video: 🤍 Alex Bellos books (including colouring books): 🤍 Colouring by Tiffany Arment: 🤍 (or coloring as it is America!) Thanks to Loretta Kolakoski for pictures of William (Bill). OEIS entry: 🤍 Oldenburger paper (1939) pre-dating Kolakoski: 🤍 (the sequence is sometimes named for Oldenburger too) Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): 🤍 We are also supported by Science Sandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science. NUMBERPHILE Website: 🤍 Numberphile on Facebook: 🤍 Numberphile tweets: 🤍 Subscribe: 🤍 Videos by Brady Haran Patreon: 🤍 Brady's videos subreddit: 🤍 Brady's latest videos across all channels: 🤍 Sign up for (occasional) emails: 🤍
value shown is frequency played, 10 times the number in the sequence
Construct Recamán’s Sequence programmatically (Live Example): Recamán’s sequence
Each number in the Recaman sequence is represented in base 1+ sqrt(2) and the digits (0,1,2) in this representation are played as a chord: '1' digit means that the note is played by a single instrument and '2' means that it is played by two instruments. A '2' is shown by a color bar inside of a color bar.
The legendary John H. Conway on properties he discovered within the so-called Look-and-Say Sequence. Conway Playlist: 🤍 More links & stuff in full description below ↓↓↓ More Conway videos: 🤍 Support us on Patreon: 🤍 NUMBERPHILE Website: 🤍 Numberphile on Facebook: 🤍 Numberphile tweets: 🤍 Subscribe: 🤍 Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): 🤍 Videos by Brady Haran Brady's videos subreddit: 🤍 Brady's latest videos across all channels: 🤍 Sign up for (occasional) emails: 🤍 Numberphile T-Shirts: 🤍 Other merchandise: 🤍
Generative Art created using Processing. As part of a series of works based around curves - this one creates a series of visualisations of the Recaman Sequence. “In mathematics and computer science, the Recaman sequence is a well-known sequence defined by a recurrence relation. Because its elements are related to the previous elements in a straightforward way, they are often defined using recursion.” (Extract from Wikipedia). In simple mathematical terms, it is the sequence, starting with 0 and then a(n) formed by letting: a(n) = a(n-1) - n but only if a(n-1) – n is greater than 0 and is new (i.e. not previously seen in the sequence) otherwise, a(n) = a(n-1) + n. The first few terms are 0, 1, 3, 6, 2, 7, 13, 20, 12, 21, 11... It has been succinctly defined as "subtract if you can, otherwise add." I have added more details and background at the end of this description for those that are interested. In 2018, the Numberphile YouTube channel published a video titled “The Slightly Spooky Recamán Sequence”, showing a visualization using “alternating” semi-circles. It is this foundation upon which my visualisations are broadly based, with some variations. In my work, there are 3 main variations, based on the first 800 or so terms of the sequence. The first draws semi-circle arcs, alternating in direction, as in the original Numberphile video, only using a different colour scheme. The second draws triangular shapes on a similar basis, but with the height of each triangle set using a random element. The third draws a series of full circles, with each diameter being set by pairs of consecutive numbers from the sequence. As each of the sequences used in the visualisations are quite long, I use a scaling factor to maximise what is displayed on the screen. I also redraw, in reverse, the full sequence at each step, as this avoids losing the early smaller details. At the very end of the video, again, for those that are interested, I have added a short visualisation of just the first 60 numbers in the sequence in “slower” motion, as this makes it a little easier to follow what is happening. A video of Generative Art can only show a snapshot of the work; the full computer code version generates an infinite set of Recaman Sequence Visualisations. The music track is Time to Spare by An Jone; taken from the YouTube Studio Audio Library. If you appreciate this work, please "Like" it and also subscribe to my channel. This will help encourage me to produce further works and publish them. Thank you, Steve More Background and Maths Stuff. Recamán's sequence was named after its inventor, Colombian mathematician Bernardo Recamán Santos, by Neil Sloane, creator of the On-Line Encyclopaedia of Integer Sequences (OEIS). The OEIS entry for this sequence is A005132. Recamán's sequence (or Recaman's sequence): a(0) = 0; for n greater than 0, a(n) = a(n-1) - n if non-negative and not already in the sequence, otherwise a(n) = a(n-1) + n. The first terms of the sequence are: 0, 1, 3, 6, 2, 7, 13, 20, 12, 21, 11, 22, 10, 23, 9, 24, 8, 25, 43, 62, 42, 63, 41, 18, 42, 17, 43, 16, 44, 15, 45, 14, 46, 79, 113, 78, 114, 77, 39, 78, 38, 79, 37, 80, 36, 81, 35, 82, 34, 83, 33, 84, 32, 85, 31, 86, 30, 87, 29, 88, 28, 89, 27, 90, 26, 91, 157, 224, 156, 225, 155, ... Take the step number and where we are in the sequence. Try to go backwards; do this if result is above 0 and not already in the sequence – otherwise you must add and go forwards: Start with 0 in the sequence. Step Number is 1 = sequence is at 0. 0 minus 1 would be -1 so cannot go back. Therefore 0 + 1 = 1 which is added to sequence. Step Number is 2 = sequence is at 1. 1 minus 2 would be -1 so cannot go back. Therefore 1 + 2 = 3 which is added to sequence. Step Number is 3 = sequence is at 3. 3 minus 3 would be 0 so cannot go back. Therefore 3 + 3 = 6 which is added to sequence. Step Number is 4 = sequence is at 6. 6 minus 4 is 2 so WE CAN GO BACK. Therefore 6 - 4 = 2 which is added to sequence. And so on… Sloane has conjectured (in 1991) that every number eventually appears, but it has not been proved. Even though “10 to power of 230” terms have been calculated (as at 2018), the number 852,655 has not (yet?) appeared on the list.
This video ilustrates the first 650 terms or so of the Recamán's sequence. The botton colorbar represents the achieved numbers in each iteration. Yup... Things got a it boring after the 50th or so term! Done in Matlab. Code for the sequence generator (Yup, it's that easy): 🤍 Code for the animator. It can animate any sequence as alternating semicircles: 🤍 Please, like if you download! Music by: 🤍bensound.com
Recamán’s sequence, is a sequence of natural numbers in which the zeroth number is zero and the nth number adds or subtracts n from the previous number, subtracting if that would lead to a new value and adding otherwise. I created a composition by using a variation of the formula and it's values as notes. The result somehow resembles the works of György Ligeti, creepy and unsettling. 🤍
Made with After Effects and Expressions. Inspired by Numberphile. 🤍
Recaman's sequence Try to solve: 🤍 A(i)={ 0 if i=0 { A(i−1)−i if A(i−1)−i greater than 0 and not already in the sequence { A(i−1)+i otherwise. Recaman sequence: 0, 1, 3, 6, 2, 7, 13, 20, 12, 21, 11, 22, 10, 23, 9, 24, 8, 25, 43, 62, 42, 63, 41, 18, 42, 17, 43, 16, 44, 15, 45, 14, 46, 79, 113, 78, 114, 77, 39, 78, 38, 79, 37, 80, 36, 81, 35, 82, 34, 83, 33, 84, 32, 85, 31, 86, 30, 87, 29, 88, 28, 89, 27, 90, 26, 91, 157, 224, 156, 225, 155,...etc., Input: 6 Output: 0 1 3 6 2 7 Input: 20 Output:0 1 3 6 2 7 13 20 12 21 11 22 10 23 9 24 8 25 43 62 Intput:10 Output: 0 1 3 6 2 7 13 20 12 21
This is a second attempt at a 2-dimensional version of the Recamán sequence. You start on (0,0) and move around on non-negative integer grid points. In each step you try to get as close as possible to the origin without getting to a point you already touched and with a minimal (but positive) increase of the traveled distance from the last point to the next. Music: Beginning of "Free will possession" by XTaKeRuX licensed under a Attribution License. (Link: 🤍 This Video is licensed under a Attribution-NonCommercial-ShareAlike License. (🤍
The geometric Recamán Seguence is a recusively defined sequence: a_1 = 1 a_n = a_{n-1}/n if that´s integer or =a_{n-1}*n otherwise So colloquially speaking: If possible, divide by n, otherwise multiply by n. Horizontally we have a logarithmic number line. Successive elements of the sequance are connected by half circles. The winding number of a positon determines the color. This is based on Edmund Hariss' representation of the arithmetic Recamán sequence explained in this numberphile video: 🤍 Music: "SONNIK 5.17" by SONNIK licensed under a Attribution-NonCommercial-ShareAlike License. (Link: 🤍 This Video is also licensed under a Attribution-NonCommercial-ShareAlike License. (🤍
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