Some nice cellular automata :)
I explored the concept of dynamic cellular automata in my bachelor's thesis.
It is simply an extension of the classical definition of cellular automata through their evolution's polynomial (considering products of polynomials).
Below every image you can find their evolution's polynomial.
(1+x)(1+x+x^2)(1-x+x^2).png)
(x)(1+x)(1+x+x^2)(1-x+x^2)
(x^-2+x^-1+1)(1+x+x^2).png)
(x+x^2+x^3)(x^-2+x^-1+1)(1+x+x^2)
.png)
(x+x^2+x^3+x^4+x^5+x^6)
.png)
Euler's pentagonal number theorem codified in a cellular automata
(1+x).png)
(1+x+...+x^6)(1+x)
(x^-1+x^1).png)
(1+x^2+x^4+x^6)(x^-1+x^1)
 o (0,1).png)
N_t = (-1,0) or (0,1)
 o (-1,1).png)
N_t = (-1,0,1) or (-1,1)
 o (0,...,2^8).png)
N_t = (-2^8, .., 0) or (0,...,2^8)
 o (0,...,2^9).png)
N_t = (-2^9, .., 0) or (0,...,2^9)
.png)
N_t = (-t,...,0,...,t)
.png)
N_t = (-t,0,t)
(1+x+x^2+x^3+x^4+x^5).png)
(x)(1+x+x^2+x^3+x^4+x^5)
(1+x+x+x^2+x^2+x^3).png)
(x-x^2+x^3)(1+x+x+x^2+x^2+x^3)
(x^-2+1+x+x^2+x^3+x^4).png)
(x^2)(x^-2+1+x+x^2+x^3+x^4)