To make the mapping from N large numbers to cross-stitch patterns, I could, in theory, design N different patterns and then manually map them (0000000001 → design 1, 000000002 → design...). But given that encryption requires very large numbers, this would be incredibly time-consuming. Instead, I want to define a smaller set of variables that can be randomly altered to generate a large set of designs. The simplest solution to this problem would be to simply randomly place single stitches on a square grid of size sqrt(N!). However, I wanted the patterns to look closer to traditional cross-stitch, so I needed to define "units" of cross-stitch patterns. I looked at samplers, existing patterns, and pixel art to identify common components. I ended by choosing the following variables to randomize:
Some image examples I drew inspiration from are below:
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