Edge Cellular Automata

Edge Cellular Automata

J. Gravner and D. Griffeath

The latest version of the paper Robust periodic solutions and evolution from seeds in one-dimensional edge cellular automata.
This work was partially supported by the National Science Foundation and the Republic of Slovenia′s Ministry of Science.

Links to cellular automata simulation software: MCell, Golly.

The Stage I label tree text files below list each numbered node, its generations, parent and children (if any), its label, and, when it is a leaf, reason for no children. When the final Stage I tree exists, we also provide its picture. Output of an R-algorithm is in the RPS information files. For each entry, the first line includes the handle and link sizes, and the density of the pattern. The following lines form an rle input file, recognized by Golly, and ending with !. The rest of the entry gives binary handle+link data for each of the π temporal shifts. (Here, π is not reduced so any file includes RPS of all lower temporal periods.)

Range 2 examples (in parentheses, Wofram code for the elementary cellular automaton with the listed left edge dynamics); the red letter that follows indicates the class (see Section 8 of the paper):

E000 (Rule 2) B
- Stage I tree for π=4
- final Stage I tree (π₀=1)
E001 (Rule 194) B
- Stage I tree for π=4
- final Stage I tree (π₀=1)
E00D (Rule 66) B
- Stage I tree for π=4
- final Stage I tree (π₀=1)
E00E (Rule 130) B
- Stage I tree for π=4
- final Stage I tree (π₀=1)
E010 (Rule 50) P
- Stage I tree for π=4
- final Stage I tree (π₀=1)
- RPS information for π=4
E011 (Rule 242) P
- Stage I tree for π=4
- final Stage I tree (π₀=1)
- RPS information for π=4
E01D (Rule 114) P
- Stage I tree for π=4
- final Stage I tree (π₀=1)
- RPS information for π=4
E01E (Rule 178) P
- Stage I tree for π=4
- final Stage I tree (π₀=1)
- RPS information for π=4
E0D0 (Rule 18) R
- Stage I tree for π=4
E0D1 (Rule 210) R
- Stage I tree for π=4
E0DD (Rule 82) R
- Stage I tree for π=4
E0DE (Rule 146) R
- Stage I tree for π=4
E0E0 (Rule 34) B
- Stage I tree for π=4
- final Stage I tree (π₀=1)
E0E1 (Rule 226) B
- Stage I tree for π=4
- final Stage I tree (π₀=1)
E0ED (Rule 98) B
- Stage I tree for π=4
- final Stage I tree (π₀=1)
E0EE (Rule 162) B
- Stage I tree for π=4
- final Stage I tree (π₀=1)
E100 (Rule 14) B
- Stage I tree for π=4
- final Stage I tree (π₀=1)
E101 (Rule 206) P
- Stage I tree for π=4
- final Stage I tree (π₀=1)
- RPS information for π=4
E10D (Rule 78) P
- Stage I tree for π=4
- final Stage I tree (π₀=2)
- RPS information for π=4
E10E (Rule 142) B
- Stage I tree for π=4
- final Stage I tree (π₀=1)
E110 (Rule 62) P
- Stage I tree for π=4
- final Stage I tree (π₀=1)
- RPS information for π=4
E111 (Rule 254) P
- Stage I tree for π=4
- final Stage I tree (π₀=1)
- RPS information for π=4
E11D (Rule 126) R
- Stage I tree for π=4
E11E (Rule 190) P
- Stage I tree for π=4
- final Stage I tree (π₀=1)
E1D0 (Rule 30) C
- Stage I tree for π=4
- Stage I tree for π=8
- Stage I tree for π=16 (155M)
E1D1 (Rule 222) P
- Stage I tree for π=4
- final Stage I tree (π₀=1)
- RPS information for π=4
E1DD (Rule 94) C
- Stage I tree for π=4
- RPS information for π=4
- Stage I tree for π=8
- RPS information for π=8
- Stage I tree for π=16
- RPS information for π=16
- Four MCell experiments: π=32, σ=32,, π=16, σ=16, mixed-replicator-like, chaotic.
E1DE (Rule 158) P
- Stage I tree for π=4
- final Stage I tree (π₀=2)
E1E0 (Rule 46) B
- Stage I tree for π=4
- final Stage I tree (π₀=1)
E1E1 (Rule 238) P
- Stage I tree for π=4
- final Stage I tree (π₀=1)
- RPS information for π=4
E1ED (Rule 110) C
- Stage I tree for π=4
- Stage I tree for π=8
- Stage I tree for π=16
- Stage I tree for π=32
- RPS information for π=32
- Four MCell experiments: singleton, π=32, σ=16, π=32, σ=160, π=64.
E1EE (Rule 174) B
- Stage I tree for π=4
- final Stage I tree (π₀=1)
ED00 (Rule 6) B
- Stage I tree for π=4
- final Stage I tree (π₀=2)
ED01 (Rule 198) P
- Stage I tree for π=4
- final Stage I tree (π₀=2)
- RPS information for π=4
ED0D (Rule 70) P
- Stage I tree for π=4
- final Stage I tree (π₀=2)
- RPS information for π=4
ED0E (Rule 134) B
- Stage I tree for π=4
- final Stage I tree (π₀=2)
ED10 (Rule 54) C
- Stage I tree for π=4
- final Stage I tree (π₀=2)
ED11 (Rule 246) P
- Stage I tree for π=4
- final Stage I tree (π₀=2)
- RPS information for π=4
ED1D (Rule 118) P
- Stage I tree for π=4
- final Stage I tree (π₀=4)
- RPS information for π=4
ED1E (Rule 182) R
- Stage I tree for π=4
EDD0 (Rule 22) C
- Stage I tree for π=4
- Stage I tree for π=8
- RPS information for π=8
- Stage I tree for π=16
- Stage I tree for π=32 (45M)
- RPS information for π=32 (1.5M)
- Much more on the Exactly 1 page.
EDD1 (Rule 214) P
- Stage I tree for π=4
- final Stage I tree (π₀=2)
EDDD (Rule 86) C
- Stage I tree for π=4
EDDE (Rule 150) R
- Stage I tree for π=4
EDE0 (Rule 38) B
- Stage I tree for π=4
- final Stage I tree (π₀=2)
EDE1 (Rule 230) P
- Stage I tree for π=4
- final Stage I tree (π₀=2)
- RPS information for π=4
EDED (Rule 102) R
- Stage I tree for π=4
EDEE (Rule 166) B
- Stage I tree for π=4
EE00 (Rule 10) B
- Stage I tree for π=4
- final Stage I tree (π₀=1)
EE01 (Rule 202) P
- Stage I tree for π=4
- final Stage I tree (π₀=1)
- RPS information for π=4
EE0D (Rule 74) B
- Stage I tree for π=4
- final Stage I tree (π₀=2)
EE0E (Rule 138) B
- Stage I tree for π=4
- final Stage I tree (π₀=1)
EE10 (Rule 58) P
- Stage I tree for π=4
- final Stage I tree (π₀=1)
EE11 (Rule 250) P
- Stage I tree for π=4
- final Stage I tree (π₀=1)
- RPS information for π=4
EE1D (Rule 122) R
- Stage I tree for π=4
EE1E (Rule 186) P
- Stage I tree for π=4
- final Stage I tree (π₀=1)
EED0 (Rule 26) R
- Stage I tree for π=4
EED1 (Rule 218) P
- Stage I tree for π=4
- RPS information for π=4
EEDD (Rule 90) R
- Stage I tree for π=4
EEDE (Rule 154) R
- Stage I tree for π=4
EEE0 (Rule 42) B
- Stage I tree for π=4
- final Stage I tree (π₀=1)
EEE1 (Rule 234) P
- Stage I tree for π=4
- final Stage I tree (π₀=1)
- RPS information for π=4
EEED (Rule 106) C
- Stage I tree for π=4
- Two MCell experiments: sublinear, chaotic.
EEEE (Rule 170) B
- Stage I tree for π=4
- final Stage I tree (π₀=1)

Range 3 totalistic examples:

Tot 1
- Stage I tree for π=32 (31M)
- RPS information for π=32 (3.4M)
Tot 12
- Stage I tree for π=16
- RPS information for π=16
Tot 14
- Stage I tree for π=16
- RPS information for π=16
Tot 124
- Stage I tree for π=16
- RPS information for π=16
Tot 134
- Stage I tree for π=8
- final Stage I tree (π₀=8)
- RPS information for π=8