Collatz Meets Escher
Автор: Jon Seymour
Загружено: 2026-02-22
Просмотров: 32
Описание:
This video shows the evolution of 3x+5, x/2 as a plot on the x vs delta k plane.
Every Collatz like cycle element satisfies the identity:
x.d = q.k
where x is the cycle element, d is the cycle modulus, q is the additive term (here 5) and k is constant that encodes the path operations on the cycle from x=23 back to itself (1 for 3x+q, 0 for x/2)
delta k here is the (k - \hat{k}) where \hat{k} = 3^3 - 2^5
The Escher-like quality of the resulting animation was a completely unintended consequence of algorithm doing its thing. For more details, see this Reddit discussion:
https://www.reddit.com/r/Collatz/comments/... and related documents.
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