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![Page 1: Research Into the Time Reversal of Cellular Automata Team rm -rf / Daniel Kaplun, Dominic Labanowski, Alex Lesman.](https://reader036.fdocuments.us/reader036/viewer/2022062802/56649ef35503460f94c05c15/html5/thumbnails/1.jpg)
Research Into the Time Reversal of Cellular Automata
Team rm -rf /Daniel Kaplun, Dominic Labanowski,
Alex Lesman
![Page 2: Research Into the Time Reversal of Cellular Automata Team rm -rf / Daniel Kaplun, Dominic Labanowski, Alex Lesman.](https://reader036.fdocuments.us/reader036/viewer/2022062802/56649ef35503460f94c05c15/html5/thumbnails/2.jpg)
Presentation Overview
Introduction to Cellular Automata
What exactly is our project?
What approaches did we use?
What were our final results?
Project summary
![Page 3: Research Into the Time Reversal of Cellular Automata Team rm -rf / Daniel Kaplun, Dominic Labanowski, Alex Lesman.](https://reader036.fdocuments.us/reader036/viewer/2022062802/56649ef35503460f94c05c15/html5/thumbnails/3.jpg)
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.
![Page 4: Research Into the Time Reversal of Cellular Automata Team rm -rf / Daniel Kaplun, Dominic Labanowski, Alex Lesman.](https://reader036.fdocuments.us/reader036/viewer/2022062802/56649ef35503460f94c05c15/html5/thumbnails/4.jpg)
Examples
• Here are some simple examples to demonstrate cellular automata rules and actions:
• Example 1: Conway’s(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
1 2 2 1 0
1 2 3 3 1
1 4 4 3 1
0 2 2 3 1
0 1 1 1 0
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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.
![Page 7: Research Into the Time Reversal of Cellular Automata Team rm -rf / Daniel Kaplun, Dominic Labanowski, Alex Lesman.](https://reader036.fdocuments.us/reader036/viewer/2022062802/56649ef35503460f94c05c15/html5/thumbnails/7.jpg)
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 2^65511 combinations, only 3^72 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
![Page 16: Research Into the Time Reversal of Cellular Automata Team rm -rf / Daniel Kaplun, Dominic Labanowski, Alex Lesman.](https://reader036.fdocuments.us/reader036/viewer/2022062802/56649ef35503460f94c05c15/html5/thumbnails/16.jpg)
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.