Chromatic percolation in two-dimensional multitype particle systems with extended-range homotypic repulsion

Cells in many tissues repel like neighbors over extended ranges, yet standard jamming models ignore this diversity. We introduce chromatic percolation-the percolation of like-type particles driven by extended-range homotypic repulsion in multitype assemblies-and map its relation to mechanical jamming. Using large-scale two-dimensional simulations, we vary the number of particle types and the packing fraction to chart a phase diagram with a mechanical jamming line (J-line) and a geometric percolation line for homotypic clusters (P-line). The jamming threshold increases with diversity and approaches the achromatic limit at large diversity, showing that more diverse systems pack more densely before becoming rigid. Despite this shift, the critical behavior at jamming is unchanged across diversity: residual energy and pressure follow the standard jamming scalings, indicating that the interaction potential-rather than diversity-sets the universality. Homotypic clustering underlies chromatic percolation. At low packing fraction, homotypic contacts dominate, the P- and J-lines nearly coincide, and rigidity and homotypic connectivity arise together. At high packing fraction, heterotypic contacts carry mechanical stability while homotypic connectivity lags; the P-line separates from the J-line and appears as a distinct geometric transition. These results reveal how particle diversity tunes where rigidity onsets while preserving how systems jam. They offer testable predictions for tissues with type-specific interactions and for programmable colloids, and they suggest design routes to materials with tailored mechanical response by controlling diversity and interaction range.