Abelian Sandpile, 27x27 all-1s recurrent configuration

thingiverse

This is a 3D model of an Abelian sandpile recurrent configuration that you can learn more about on Wikipedia: https://en.wikipedia.org/wiki/Abelian_sandpile_model#Transient_and_recurrent_configurations. It's a simple deterministic diffusion model that produces striking fractal configurations with ease. This model is designed to be printed using a multimaterial printer, and I used the MK3S+MMU2S for this project. In the language of the sandpile, this model represents the recurrent configuration equivalent to the all-1s configuration on a 27x27 square grid. The height corresponds to the value of the negative toppling function, while the color indicates the laplacian at that point. For standard definitions of the sandpile on the 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 used in this model follow the conventions outlined in a paper available here: https://arxiv.org/abs/1708.09432. This object depicts the left-most solution from Figure 1. This model is designed to print at .2mm layer height, and I've also made it possible to print an 81x81 solution as a separate model.