Sounds of the Collatz Conjecture, Part 2: Generating Raw Frequencies
Using sequences from the famous unsolved Collatz conjecture to generate audio sequences of raw frequencies.
Part 1: • Sounds of the Collatz Conjecture: Generati...
The Collatz conjecture is also known as the 3n + 1 problem, the 3x + 1 problem, the Ulam conjecture, Kakutani's problem, the Thwaites conjecture, Hasse's algorithm, or the Syracuse problem.
Three different strategies are used to map the "hailstone sequences" into sequences of frequencies: multiplying each hailstone number by a "base frequency"; multiplying each hailstone number by an increment frequency and adding it to a base frequency; and a logarithmic mapping.
An attack, decay, sustain, release (ADSR) envelope is used on pure sine waves to generate the tones, followed by a gentle low-pass filter to smooth out the perceived loudness across the frequency range.
These visualizations were written in Java using a graphical library called Processing (https://processing.org/).
0:00 The Collatz Conjecture Recap
0:53 Strategy No. 1
3:51 Strategy No. 2
6:32 Strategy No. 3
#math #music #microtonal #musictheory #unsolved #patterns #code #java #software #computerscience #visualization #algorithmicmusic #algorithmiccomposition #part2