Take a real flatworm (planaria) cut it in two halves. The part with the head will grow a tail and the other half will grow a head. The CA flatworm responds in a different way. Its head will grow a tail. The cells below the cut cannot grow a head.  In order to do that they have to get younger and younger until they become a zygote.  Which is impossible since aging is irreversible. Cells below the cut continue aging until they die.


This putative "getting younger" is called in medicine  de-differentiation. As cancer cells evolve they become more aggressive and appear younger. Their aggressiveness is attributed to  de-differentiation. Which is meaningless since cells cannot age backward. Cancer cell ages and differentiates, like any other cell.. Since aging cannot be reversed, what appears as de-differentiation is another differentiation state.

Swarm Intelligence

The CA-flaworm might still behave like  her real sister.. How does planaria's tail grow a head? Obviously not by de-differentiation. Scattered in her body are stem  cells capable of generating an entire worm.  One of them assumes control, starts proliferating, creating an embryonal organ called blastema , which gradually differentiates into a head. The same happened to the CA-worm. After the cut, nearly all cells in the layer below died except one who became a zygote, and generated a new worm.


This experiment indicates that cells remember their differentiation state, and the newly generated tail may be regarded as marker of this state. In other words, cells have a memory, which can be read by planting them, and observing their growing tails. Imagine the following procedure:
Cut a CA into slices and let them grow. Each will grow a different tail. Tail structure indicates the state of the original slice.
2. Create a slice-tale library (or dictionary). With this mapping you can uniquely deduce a state from the tail morphology, even if you do not know the slice structure. Slice planting may be regarded as a device for memory reading, or as an output. This procedure is particularly useful for extremely complex slices.


CA specification

In the universe of totalistic CAs (k=3, r=1, v. Wolfram's book), two number strings uniquely specify a 1D-CA,  {rule, and initial conditions}. In 2D-CAs we have to specify also the cell age distribution at death.  2D-CA= {rule,  initial conditions, cell age distribution at death}.

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