Abelian Sandpile, 81x81 all-1s recurrent configuration

thingiverse

This is a 3d model of an Abelian sandpile recurrent configuration. You can read some about the Abelian sandpile model on wikipedia: https://en.wikipedia.org/wiki/Abelian_sandpile_model#Transient_and_recurrent_configurations It is a simple deterministic diffusion model which can produce striking fractal configurations. THIS MODEL IS DESIGNED TO BE PRINTED WITH A MULTIMATERIAL PRINTER. I used the MK3S+MMU2S. In the language of the sandpile, this model is the recurrent configuration equivalent to the all-1s configuration on a 81x81 square grid. The height is the value of the (negative) toppling function; the color indicates the laplacian (grains of sand) at that point. For the 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 -1,0,1,2 follow the conventions in this paper: https://arxiv.org/abs/1708.09432 Note that this object depicts the second solution in Figure 1. The model is made to print at .2mm layer height. The 27x27 solution is available as a separate thing.