3 ms·

This is independent work. Probably fits in with fractals and L-systems.

• agumonkey 9y ago
  So that was all you had in mind as a starting point ? again, lovely article, got inspired by ti
  • tylerneylon 9y ago
    That's all the solid work I have so far. Tons of ideas for what could be next. For example, consider convolutions on sets generated by L-systems (eg the Cantor set). I suspect those might offer continuous, finitely-supported, linearly-shifted self-replicating fns (the current article is mainly about non-linear shifts; t_1 is only piecewise linear). Maybe L-systems even completely characterize that category of self-replicating fns. Other ideas: * Higher dimensions (eg f1 + f2 + f3 = g with domain R^2) * Shifted fns f1, f2 whose sum has surprisingly small diff from their sum: ie small |C(f1+f2)-shift(f1)|; the normal fn appears to fall into this category
    • agumonkey 9y ago
      as in elf similarity across projection, a R^n composition that ends up a as a function on R^N-1 ?