Research Into the Time Reversal of Cellular Automata

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Research Into the Time Reversal of Cellular
Automata

• Team rm -rf /
• Daniel Kaplun, Dominic Labanowski, Alex Lesman

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Presentation Overview

• Introduction to Cellular Automata
• What exactly is our project?
• What approaches did we use?
• What were our final results?
• Project summary

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What Are Cellular Automata?

• What are they?
• Algorithm-controlled single cell life / death
  simulations
• How does it work?
• A set of rules (often seen as life / birth)
  dictates the actions of a cell based on the
  number of neighbours surrounding it.

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Examples

• Here are some simple examples to demonstrate
  cellular automata rules and actions
• Example 1 Conways
• (23 / 3)
• Example 2 Artsy
• (01245678/34 )

• Example 1
• Example 2

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Detail

• This is an example of the 23/3 rule set (the
  original) of game of life
• a dead cell with 3 neighbors is born
• a live cell with 2 or 3 neighbors lives.
• Otherwise the cells are dead

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What is our project?

• Simple shapes with simple rules can create
  massive and complicated patterns.
• Our initial goal was to find the seed of a 256
  x 256 Mona Lisa picture after a series of
  calculations proved this impossible, it was our
  decision to instead move the OSC logo back 3
  generations in 2 different ways.
• A multitude of different approaches were tested,
  none were successful in attaining our ultimate
  goal.

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Attempted Automata Reversal Techniques

• Total brute force
• Serial (exponential time growth)
• Parallel try 1 (recombination difficulties)
• Random placement
• Both (exponential decay of probability)
• Ruleset manipulation
• Both (limited coding time)
• Parallel Brute force(v2) finally yielded results
  (sort of)
• Parallel Brute force(v3) yielded results as well
  (sort of)

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Brute Force Technique

• Serial Size Increase Difficulties
• Exponential time increase as grid increases
• 5 x 5 grid 0.35 seconds
• 6 x 6 grid 11 hours 56 minutes 48 seconds
• 7 x 7 grid 2 months, 5 days, 23 hours, 7
  minutes
• 10 x 10 grid 413,564,066,800,000 years
• 256 x 256 grid ?

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Brute Force Technique

• Masses of possibilities
• Over 150 possibilities for a 6 cell pattern on a
  5 x 5 grid.
• The number of possibilities also increases
  exponentially with the size of the grid.
• Too many to keep track of.

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Brute Force TechniqueParallel

• Parallel Reconstitution Difficulties
• Buffer overlap
• Seemingly Impossible to correct

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Recombination Problems

• Cut into pieces
• 
  
• Backward one step
• !

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Random Placement

• Very promising initially
• Used the amount of live cells 1 as the input
  image
• However, probability decreased exponentially
• 4 x 4 grid 1 112
• 5 x 5 grid 1 259,170
• The process was never perfected the program
  never returned positive results.

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Rule Manipulation

• Instead of brute-forcing pixels, brute- forcing
  sets of rules in order to see if any rulesets can
  be used as identities.
• Instead of 265511 combinations, only 372
  combinations for our Mona Lisa.
• Unable to complete code in time, conceptually
  difficult to grasp.

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Parallel Brute Force (v2)

• Rewrote code to make it much (thousands of times)
  more efficient
• Ran on many processors, splitting up the work
• Linear time savings
• Allowed us to do 6 x 6 grids vs. 5 x 5 grids
• Very easy (in theory) to go back multiple
  generations

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Brute Force Technique (v3)

• Parallel processed, when one processor finds a
  result it tells the others to stop
• Using STL (Standard Template Library)
  2-Dimentional vectors because of their dynamic
  expandability
• The problem with going backwards is the expansion
  of the grid
• Used C bitwise operators to create sample grids

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Final Results

• Moved the OSC logo back 3 generations
• Manually selected preferred steps from optimized
  lists
• Computed combinations with minimal expansion

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Project Summary

• Initial goals unreachable
• Second set of goals attempted with multiple
  approaches, brute force (v3) was found to be the
  most effective
• With further investigation a more feasible
  back-in-time approach could still be possible,
  but looks very unlikely when using large sizes.