Chaotic CA

In the following image the second CA was planted at t = 20 and distance =18. The result is an immortal chaotic CA. The graph depicts its  mass accumulation (production).The result is an immortal chaotic CA. The graph depicts its mass accumulation (production).
Please note:
- Each CA by itself is mortal, only their interaction makes them immortal.
- The chaotic CA generates non chaotic and immortal progeny (attractors).
- The CA group expands indefinitely.

Compare it with the Lorenz attractor which does not generate non-chaotic processes. You may wonder, what is the difference between the two chaotic phenomena? Currently you lack means (tools) to distinguish between them. To me, the Lorenz attractor fails to capture (portray) chaotic phenomena of life.

Interaction with a barrier

The barrier(vertical line) is made of the number 2. In the first history there is no interaction. In the second the seed is planted 26 units from the barrier. As the CA grows it approaches the barrier and covers it with CAs (cells). In the third history the CA covers the barrier with a membrane (without cells) and bounces back to a remote niche (attractor).

The first history illustrates how epithelial cells cover the bottom of a Petri dish.(which is positioned vertically). Initially the cells (CAs) float in the medium and later they adhere to the dish bottom.  In the second history, cells move away from the Petri dish bottom  which is the typical behavior of cancer cells. This history illustrates also how cells cover the Petri dish bottom with a membrane made of two layers, black (=2), and gray (=1).

The next image illustrates the interaction between  a CA and a barrier made of the number 0.  As the CA grows it approaches the barrier. The CA boundary which touches the barrier is destroyed (=0). After a while the CA starts moving away from the barrier, restoring its integrity. In the next history the seed was planted closer to the barrier. As the CA approaches the barrier, it loses more and more substance until it dies.

This experiment illustrates the behavior of an ameba that approaches a toxic substance. Initially it loses part of its cytoplasm. Later on it retreats and regenerates its cytoplasm. The second ameba (history) hit the poison earlier than the previous one. It was younger, had less resources, and ultimately died.

Previous page
Next page