Message Boards Message Boards


[WSS22] Multiway mobile automata

Posted 8 months ago
3 Replies
12 Total Likes

enter image description here

POSTED BY: Felipe Amorim
3 Replies

This one shows the first rule that applies to the first active cell, the second rule that applies to second active cell, and so on. Given a collection of cells on a state for which the system is given rules that can generate multiple outputs which can be expected to generate more possibilities of connectivity, one cell can be updated at each step.

With[{g = MultiwayMobileAutomaton[{{275, 999}, {81, 384}},
    {{ConstantArray[0, 35], 17}}, 5, "StatesGraphStructure", 
    VertexSize -> 0.5]},
 HighlightGraph[g, {VertexOutComponent[g, VertexList[g][[1]], 2]}]]

Combine Randomly Chosen Rules

You can combine rules for more connectivity in the multiway systems, like how 4 rules are combined & update the states 6 times or how you're getting all these rules within a specific combination of cells. Did you know that branchial graphs are accurate, ahistorical or as the rules apply in one step?

g = MultiwayMobileAutomaton[{{275, 999}, {81, 
    384}}, {{ConstantArray[0, 11], 5}}, 3, "StatesGraph", 
  VertexSize -> 1]

States Depiction

Running the systems for a few more steps, one can start to see more complex stuff at each step when we see more branching and merging and just want to know what part of the orbit it's going to be. Representing the position of the active cells after an update (grey or white), mapping those three blocks of state via rules that will be specified as a list of two numbers to where the updated cell will turn after an update, and also as a binary list.

g = MultiwayMobileAutomaton[{{275, 999}, {81, 
    384}}, {{ConstantArray[0, 34], 16}}, 15, "StatesGraphStructure", 
  VertexSize -> 0.5]

Active State Graph Structure

Ordinarily, apply the same rules to the same configuration of the state being updated, which generates many possible paths of evolution. I didn't know that only one active cell could get updated at a time according to a specific rule! That's what it's like going from ordinary to multiway. It's the intermediate case between the combined rules of single-headed Mobile Automata and multi-way string substitution systems. It's like combining multiple rules of ordinary Turing Machines to create a multi-way Turing Machine.

With[{start = ToString@{ConstantArray[0, 35], 17}},
    MultiwayMobileAutomaton[rule, {start}, 7, structure, 
     VertexSize -> 1.2], start]],
  {rule, {{{700, 100}, {761, 851}}, {{295, 265}, {218, 912}}, {{21, 
      78}, {550, 788}}, {{312, 238}, {707, 502}}, {{272, 239}, {283, 
      592}} }}, {structure, {"BranchialGraphStructure", 

Multiway Mobile Automaton

I really like this post, that was some retrospective how you did it with a list of two numbers and got the color and position.

POSTED BY: Dean Gladish

Nice one man! Very beautiful! ;)

POSTED BY: Claudio Chaib

enter image description here -- you have earned Featured Contributor Badge enter image description here Your exceptional post has been selected for our editorial column Staff Picks and Your Profile is now distinguished by a Featured Contributor Badge and is displayed on the Featured Contributor Board. Thank you!

POSTED BY: Moderation Team
Reply to this discussion
Community posts can be styled and formatted using the Markdown syntax.
Reply Preview
or Discard

Group Abstract Group Abstract