AlgoMotion | Toothpick Sequence Visualized with Circle of Fifths Harmony | 256 Steps @AlgoMotion | Uploaded March 2024 | Updated October 2024, 3 hours ago.
Visualizing the Toothpick Sequence to 256 steps, with musical harmony based on the circle of fifths.
In the The On-Line Encyclopedia of Integer Sequences (OEIS), the Toothpick Sequence is sequence number A139250: oeis.org/A139250
To generate the toothpick sequence, at each step add a toothpick to the end of every "exposed" toothpick. Two toothpicks may never overlap, and the midpoint of each new toothpick must touch the endpoint of exactly one existing toothpick. An endpoint is "exposed" if it does not touch any other toothpick.
At steps of the form 2^k (powers of 2), the number of new toothpicks at those steps are equal to 2^k, and they are always placed along two lines perpendicular to the initial toothpick.
Chord Selection:
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The chords move through the circle of fifths until a "power of 2" step is reached. Each chord is selected so that every time we arrive at a "power of 2" step, the chord is a C.
The exact quality of each chord was manually selected for each pitch class (i.e. for all 12 notes). The number of notes in each chord and the MIDI velocity of each note are functions of how many new toothpicks are placed at a given step.
The code for creating this video was written in Java using the Processing graphical library (processing.org/).
________
Interested in learning more about algorithms and how to program? Here are some useful and/or classic textbooks that I recommend (these are affiliate links, if you buy one, I get a small commission):
▶ “Algorithms” (4th Edition) by Robert Sedgewick & Kevin Wayne: amzn.to/3uo25xR
▶ “Effective Java” (3rd Edition) by Joshua Bloch: amzn.to/3HOnYJL
▶ “Python Crash Course, 3rd Edition: A Hands-On, Project-Based Introduction to Programming” by Eric Matthes: amzn.to/481jQ43
▶ “Design Patterns: Elements of Reusable Object-Oriented Software” by Erich Gamma, Richard Helm, Ralph Johnson, & John Vlissides: amzn.to/49fpr7R
▶ “Discrete Algorithmic Mathematics” by Stephen B. Maurer & Anthony Ralston: amzn.to/4bmsOvG
#math #art #music #toothpick #sequence #circleoffifths #musictheory #algorithmicmusic #visualization #mathematics #cellularautomata #algorithm #java #code #computerscience #fractal #hypnotic #mesmerizing #calming #calmingmusic #audiovisual #studymusic #focusmusic
Visualizing the Toothpick Sequence to 256 steps, with musical harmony based on the circle of fifths.
In the The On-Line Encyclopedia of Integer Sequences (OEIS), the Toothpick Sequence is sequence number A139250: oeis.org/A139250
To generate the toothpick sequence, at each step add a toothpick to the end of every "exposed" toothpick. Two toothpicks may never overlap, and the midpoint of each new toothpick must touch the endpoint of exactly one existing toothpick. An endpoint is "exposed" if it does not touch any other toothpick.
At steps of the form 2^k (powers of 2), the number of new toothpicks at those steps are equal to 2^k, and they are always placed along two lines perpendicular to the initial toothpick.
Chord Selection:
=============
The chords move through the circle of fifths until a "power of 2" step is reached. Each chord is selected so that every time we arrive at a "power of 2" step, the chord is a C.
The exact quality of each chord was manually selected for each pitch class (i.e. for all 12 notes). The number of notes in each chord and the MIDI velocity of each note are functions of how many new toothpicks are placed at a given step.
The code for creating this video was written in Java using the Processing graphical library (processing.org/).
________
Interested in learning more about algorithms and how to program? Here are some useful and/or classic textbooks that I recommend (these are affiliate links, if you buy one, I get a small commission):
▶ “Algorithms” (4th Edition) by Robert Sedgewick & Kevin Wayne: amzn.to/3uo25xR
▶ “Effective Java” (3rd Edition) by Joshua Bloch: amzn.to/3HOnYJL
▶ “Python Crash Course, 3rd Edition: A Hands-On, Project-Based Introduction to Programming” by Eric Matthes: amzn.to/481jQ43
▶ “Design Patterns: Elements of Reusable Object-Oriented Software” by Erich Gamma, Richard Helm, Ralph Johnson, & John Vlissides: amzn.to/49fpr7R
▶ “Discrete Algorithmic Mathematics” by Stephen B. Maurer & Anthony Ralston: amzn.to/4bmsOvG
#math #art #music #toothpick #sequence #circleoffifths #musictheory #algorithmicmusic #visualization #mathematics #cellularautomata #algorithm #java #code #computerscience #fractal #hypnotic #mesmerizing #calming #calmingmusic #audiovisual #studymusic #focusmusic
