Investigating Transformational Complexity: Counting Functions a Region Induces on Another in Elementary Cellular Automata

Figure 1

Diagram displaying an example of the inverted light cone of the input set of cells . The input includes volume (in red) and environment (in light green). The output (in orange) contains the cells within the future light cone of that are in the Moore neighborhood of a cell outside of . The combination of yellow and orange cells denotes the future light cone of volume within . The red line shows the border between the environment's inverted light cone and the future lightcone of the volume. The vertical dashed lines show the future of the volume, and the horizontal dashed line shows the limit of computation considered at some time , in Janzing’s approach [5].