hash random emergence (v2 because the server move took down the original post)

[tommyaweosme]

(THE ORIGINAL POST HAS BECOME LOST MEDIA BECAUSE OF THE SERVER MOVE REMOVING IT)

i've invented a new rulespace known as hash random emergence. each cell looks at its own color and the rule, and it decides whether or not to spawn 1 or 2 cells around it, where they are, and what color they are, and then the cell dies.

the key property of these rules is that cells can stack infinitely. that means patterns that look like they only have around 20 cells can, in reality, have tens of thousands of cells.

by far the rarest form in any of these rules are oscillators. every oscillator has been found via automated search! period-2 oscillators came first, then 3,4,5,6,7,12,8. hash random emergence is theoretically omniperiodic, but that would require a hash that is beyond 32-bit or 128-bit, it would have to be infinity-bit.

there are also rules that emulate the powers of 2, f(n)=f(n-1)+f(n-2), f(n)=f(n-2)+f(n-3), sqrt(2), and arbitrary constants like 1.521.

edit: 1.521 turns out to be f(n)=f(n-1)+f(n-5)

there is no way to view this rulespace in lifeviewer because, yk, cells stack, but i have implemented it: https://github.com/tommyaweosme/hash-ra ... /tree/main

i hope people are interested in this new cellular automaton!

unsolved problems
- period-10 oscillator
- period-11 oscillator
- period-13 and beyond oscillator
- period 8 and beyond in less than 11 states
- camelship and other oblique ships
- abstract puffer type that cannot be made in conway's game of life under normal conditions: puffer that makes puffers that makes puffers ... to infinity
- turing-completeness