Cellular Automata rules lexicon

Go back to MCell Home

Family: 1D totalistic CA

Type: totalistic or outer totalistic with optional decay

This family allows exploring a wide range of one-dimensional totalistic Cellular Automata. The initial configuration is displayed in the top line. Each successive line reading down the screen is calculated from the line immediately above it, so Rudy Rucker's comments on CelLab apply also to MCell: "Unlike in many other programs, one-dimensional Cellular Automata implemented in MCell grow downward. If this bothers you a lot, you can turn your monitor over, although you shouldn't leave it that way for too long as it might overheat."

The user interface of the game allows specifying rules for calculating next rows of cells. The neighborhood can be specified in a range 1-10, allowing up to 21 cells to be considered. One can specify independently the totals of alive neighbors for cells to survive and to be born, in a similar to "Life" S/B manner. It's also possible to specify if the center cell should be taken into account or ignored.

The unique feature of MCell's implementation of one-dimensional totalistic CA is History. Like in "Generations" family, when history in on, cells that would simply die are getting older, up to the maximum specified state. Such cells cannot give birth to new cells, but they occupy the space of the lattice, thus changing the rules radically.

The lattice can be treated as a ring. When board wrapping is on, active cells that leave at the right edge enter again on the left edge and vice versa.

One-dimensional totalistic CA notation
The notation of one-dimensional totalistic CA rules has the "R,C,M,S,B" form, where:
R - specifies the range (1..10)
C - specifies the count of states, 0..256. A value smaller than 3 means the history is not active. Values greater than 2 activate the history, with the given count of states.
M - specifies activity of the center (middle) cell. 1 is on, 0 is off.
S - specifies a single total of neighbors allowing the cell to survive. 'S' can appear any times in the rule. Example: S2,S3,S8.
B - specifies a single total of neighbors allowing the cell to be born. 'B' can appear any times in the rule. Example: B0,B3,B4,B17

Note that randomizing the board fills only the top row of one-dimensional universe. All patterns are loaded at the top of the lattice, too. One can use all drawing tools available in the program, but only cells in the active row are taken into account. At the beginning the active row is the top row. After animating the rule the active top moves down.

MJCell Java applet is able to run all rules from this group.

MCell built-in 1-D totalistic CA rules

Name Rule (R,C,M,S,B) Description
Abacus R2,C10,M1,S0,S1,B0,B3 The rule produces vertical strings of beads, resembling abacus. Note that often the patterns stabilize, and only some beads change their position!
Found at random by Mirek Wojtowicz.
Champagne R3,C0,M1,S3,S6,S7,B0,B1 One often sees what he has on his mind, but even my wife, a total abstainer, recognizes here champagne-glasses...
Found at random by Mirek Wojtowicz.
Class 4 a R2,C0,M1,S1,S3,B2,B3,B4 An example of Wolfram's mythical Class 4 automaton.
Found at random by Mirek Wojtowicz.
Class 4 b R6,C0,M1,S3,S4,S5,S9,S11,S12,S13, B0,B1,B3,B13 An example of Wolfram's mythical Class 4 automaton.
Found at random by Mirek Wojtowicz.
Class 4 c R6,C0,M1,S3,S5,S8,S9, S11,B0,B7,B8, B9,B13 An example of Wolfram's mythical Class 4 automaton.
Found at random by Mirek Wojtowicz.
Date palms R5,C0,M1,S0,S7,S8,S9,S10,S11,B0 The small triangles produced by the rule are usually aligned, what resembles trunks of date palms.
Found at random by Mirek Wojtowicz.
Embossed triangles R2,C0,M1,S2,S3,B2,B3,B4 Sierpinski-like patterns consisting of embossed triangles.
Found at random by Mirek Wojtowicz.
Fences R6,C25,M1,S1,S4,S7,S8,B0,B3,B5 A very surprising one-dimensional automaton, producing vertical strings and irregular thick more or less horizontal stripes.
Found at random by Mirek Wojtowicz.
Forest R10,C0,M0,S1,S2,S6,S7,S9,S12, S14,S17, B1,B7,B10,B11,B13,B15, B16,B17,B19 A very beautiful rule, showing a thicket. Sometimes the trees are sparser and their trunks can be seen among branches and leaves.
Found at random by Mirek Wojtowicz.
Gears 1 R5,C0,M1,S0,S7,S10,S11,B0 The rule produces randomly placed segments of gears (toothed wheels) of all sizes.
Found at random by Mirek Wojtowicz.
Gears 2 R5,C0,M1,S0,S6,S10,S11,B0 A rule similar to Gears 1, but here gears are neatly aligned.
Found at random by Mirek Wojtowicz.
Marvel R3,C0,M0,S0,S5,S6,B0,B3 The most beautiful one-dimensional rule I've seen so far. This is how I fancied the Persian gardens when I was a child.
Found at random by Mirek Wojtowicz.
Maze R3,C10,M1,S3,S4,S5,B1,B3,B4,B5 This rule produces 3-dimensional maze, with high walls.
Found at random by Mirek Wojtowicz.
Noname01 R2,C0,M1,S0,S3,S4,B2,B4,B5 I can't tell what is this rule like. Help is appreciated.
Found at random by Mirek Wojtowicz.
Noname02 R2,C15,M1,S2,S3,B1,B2 I can't tell what is this rule like. Help is appreciated.
Found at random by Mirek Wojtowicz.
Pascal's triangle R1,C0,M1,B1 A single nonzero cell evolves to Pascal's triangle of binomial coefficients, reduced modulo 2.
A rule by Stephen Wolfram.
Porridge R1,C0,M1,S0,S3,B0,B2 This rule produces a dense soup with many small triangles.
Found at random by Mirek Wojtowicz.
Roots R4,C0,M1,S1,S2,S5,S6,S9,B3,B4,B6 This Class-4 CA produces thick tangled roots and interesting ornamental gliders.
Found at random by Mirek Wojtowicz.
Shaded Triangles R3,C3,M1,S0,S2,S3,S4, S5,S6,B3,B4,B5,B6,B7 A rule by Jason Rampe.
Skyscrapers R6,C10,M1,S2,S4,S6,S7,S8,S11, S13,B0,B1,B3,B8,B12 A big city with protruding skyscrapers watched from the bird's-eye view.
Found at random by Mirek Wojtowicz.
The City R3,C0,M0,S0,S3,B0,B4 Another city simulation, this time watched at night. Many sky-scrapers show shining windows.
Found at random by Mirek Wojtowicz.
Tulips R10,C0,M1,S0,S3,S6,S10,S11, S14,S15, S16,S17,S18,S19,S20, S21,B1,B11,B12, B17,B18,B19,B20,B21 This surprisingly beautiful rule shows large fields covered with tulips.
Found at random by Mirek Wojtowicz.
Walls R2,C15,M1,S2,S3,B1,B3 A rule very similar to Maze, yet the walls are bigger and more regular.
Found at random by Mirek Wojtowicz.
Wood Grain R8,C3,M0,S1,S2,S4,S6,S7,S10, S12,S13,S14,B0,B2,B3,B4,B5,B6, B7,B10,B11,B13,B15 A rule by Jason Rampe.

 


Webmaster: Mirek Wójtowicz
envelope info@mirekw.com,
envelope mirwoj@life.pl
globe http://www.mirekw.com


MCell mirrors:
globe USA  http://psoup.math.wisc.edu/mcell/
globe Europe  http://www.mirwoj.opus.chelm.pl

Last update: 15 Sep 2001