When a voltage is applied across a thin layer of cholesteric liquid crystal, fingers of cholesteric alignment can form and propagate in the layer. In computer simulation, based on experimental laboratory results, we demonstrate that these cholesteric fingers can solve selected problems of computational geometry, logic, and arithmetics. We show that branching fingers approximate a planar Voronoi diagram, and nonbranching fingers produce a convex subdivision of concave polygons. We also provide a detailed blueprint and simulation of a one-bit half-adder functioning on the principles of collision-based computing, where the implementation is via collision of liquid crystal fingers with obstacles and other fingers.