Identifying a class of pattern in cellular automata
In the "Star Wars" rule (345/2/4), there exist structures that expand infinitely in one dimension (usually at an angle of 45 degrees to the axes) while moving in a direction perpendicular to their expansion. What is this class of structure called?
Also, here's a small p12 oscillator that showed up while I was expirimenting with Golly's random fill feature on this rule:
I was unable to find an official list of pattern names for this rule, so, for now, I'll call this oscillator a "cross with p12 orbitter."
Game of Life on a finite, wrapping grid
Today I made a javascript implmentation of Conway's Game of Life for a finite (150 x 150), wrapping grid.
You can view it here, and the source can be found here.
Update: Optimized rendering, the random pregeneration can now generate the Toad oscilator, can now pregenerate gliders going in all four directions
Turing Machines/Deque
These are the functions for my 22-color encoding of a Deque of base-10 integers on a TM (I could cut it down to 12, but that would make it to easy to see the contents of the deque)
Input: The base-10 integer to push, followed by the encoding of the rest of the initial deque
Output: The encoding of the final deque
O(log n) time with respect to the element pushed
Optimizations on the last one are welcome.
Turing Machines
These are all designed using the rule table syntax defined here.
If the above link doesn't load, this java implementation also works (if you manually remove any comments first.)
1 state - 3 color
O(n) time with respect to bit length
This is a multi-part implementation and may be seen here.
FGH with ordinals
\(f_{0}(\omega)=\omega+1\)
\(f_{0}^{n}(\omega)=\omega+n\)
\(f_{1}(\omega)=f_{0}^{\omega}(\omega)=\omega+\omega=\omega*2\)
\(f_{1}(\omega*k+n)\;\;(k,n