Reversing Conway’s Game of Life

1. 0100 • 0110 • 0110 • 0010 Reversing Conway’s Game of Life Jonathan Goetz

2. The Rules of the Game • 1 living neighbor = cell dies • 2 living neighbors = cell maintains • 3 living neighbors = cell lives • 4-8 living neighbors = cell dies • Many states share descendants • Some states have no ancestors • Some states are their own ancestors • Information is lost In Reverse? • 0110 • 1000 • 0001 • 0110

3. Challenges • Loss of information prevents traditional back calculation of initial state • The problem itself maps rather easily to a 400 input and 400 output MLP pattern classification which is applied recursively. • 0100 • 0110 • 0110 • 0010

4. Details • The basic structure is a multilayered set of MLPs which rescales the result to a range of 0-1 before reapplying the same MLP in order to approximate the input layout. • Initial attempts to create a variable depth training weighting were not successful. • 0110 • 1000 • 0001 • 0110

5. Status • Initial attempts at rewriting the training process for between 1-5 levels of difference unsuccessful. • Instead implementing this by converting every multi-generational training data point into multiple 1 generation steps. • 0100 • 0110 • 0110 • 0010