De-differentiation
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.
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.
Memory
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:
1. 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}.