Abelian Sandpile, 81x81 all-1s recurrent configuration

thingiverse

This is a 3D model of an Abelian sandpile recurrent configuration, featuring intricate fractal patterns that can be read about in detail on Wikipedia: https://en.wikipedia.org/wiki/Abelian_sandpile_model#Transient_and_recurrent_configurations. The Abelian sandpile model is a simple deterministic diffusion model capable of producing striking fractal configurations. It's specifically designed to be printed with a multimaterial printer, and I used the MK3S+MMU2S to create this unique piece. In the language of the sandpile, this model represents the recurrent configuration equivalent to the all-1s configuration on an 81x81 square grid. The height is determined by the value of the (negative) toppling function, while the color indicates the laplacian (grains of sand) at that point. For the standard definitions of the sandpile on a square lattice, the included files - lapn1, lap0, lap1, and lap2 - correspond to 0, 1, 2, or 3 grains of sand left at each site. The numbers -1,0,1,2 follow the conventions outlined in this paper: https://arxiv.org/abs/1708.09432. This object depicts the second solution in Figure 1. It's designed to print at a layer height of .2mm, showcasing the intricate details of the Abelian sandpile recurrent configuration. A separate model featuring a 27x27 solution is also available.