Tessellation Automata

Cellular Automata in the Triangular Tessellation

For t he discussion below t he following definit ions are helpful. A semito-talistic CA rule is a rul e for a cellular aut omaton (CA) where (a) we tally t he living neighbors t o a cell without regard to their orient atio n wit h respect t o th at cell, and (b) t he ru le applied t o a cell may depend upon its current status. A lifelike rule (LFR rul e) is a semit otalist ic CA rul e where (1)...

Certain Relations between Properties of Maps of Tessellation Automata

In a different approach, Hedlund [4], Sears [13], and Ryan [12] defined the shift dynamical system and investigated the properties of the continuous transformations which commute with the shift transformations, and showed many interesting results in one-dimensional tessellation spaces. Hedlund conjectured that in some sense, the set A of all parallel maps which are injective on the set C of all...

Instanced Tessellation

Decomposition Phenomenon in One-Dimensional Scope-Three Tessellation Automata with Arbitrary Number of States

The tessellation automaton (TA) is a formalization of the concept of an infinite regular array of identical finite-state machines uniformly interconnected in the sense that each machine can directly receive information by means of interconnecting wires from a finite number of neighboring machines where the spatial arrangement of these neighboring machines is the same relative to each machine in...

Smooth GPU Tessellation

Models used in real-time graphics are commonly rendered using triangular boundary representations. Triangulation approximates flat surfaces very well, but requires many fine triangles to accurately represent curved surfaces. This project implements two methods for smoothing coarse input meshes using GPU tessellation shaders to obtain smooth surfaces.