1d Transformer like automata
solve an open-ended research task that aims to produce interesting celualr automatas
Prompt
Building interesting 2D patterns by randomly sampling from functions with local attention and iteratively applying them (with a non-linearity like binarizing)—such as image kernels—is relatively easy because the parameter space is tiny. For example, a 3x3 kernel is a 9-dimensional vector, and by sampling according to symmetries, you can explore a 4-dimensional space that densely generates diverse patterns by recursively applying the kernel and binarizing at each step. Can you write a single HTML file containing JavaScript that randomly samples parameters for an architecture using quadratic all-to-all attention (like in Transformers)? The program should recursively apply this architecture to a 1D input sequence of symbols (or a family of input sequences) to generate and display a dense variety of interesting sequences. Please focus purely on the academic problem and technical implementation rather than aesthetics.
A system prompt was added to support web rendering
