A CA facing an obstacle

The following CA (Rule #600) is controlled by six buttons:
Plant: Plants a zygote.
Shorter:  Makes CA shorter (at least one state)
Longer: Makes CA longer 
Obstacle a toggle switch which places an obstacle at x=15.
Move obstacle+ moves it downward.
Move obstacle- moves it upward.

Single state CA

Start with planting a zygote, and watch the one state CA advancing. Then click on "Longer" which determines how many states remain alive.Take for instance a 5-state CA. As the head   advances it is followed by 4 states.  State-1 equals state-0 at time = -1. State-2 equals state-0 at time = -2. Generally state[ i ]   = state[ 0, time  = - i] . These states remember what has happened to the CA up to 4 time units ago. The CA carries with it its own memory. Each state lives five time units, whereupon it dies.  CA memory continually turns over.

You may now activate the obstacle. As the CA slides under the obstacle, only the first state interacts, the memory states are not affected. They remember how the first state interacted. Interaction leads to four possible outcomes:

1. No interaction: The CA continues undisturbed.
2. A perturbation: The CA interacts and its structure changes.
3. A solution: The CA assumes its initial configuration of 46 states, or it may attain a 29 state configuration.
4. Death.

Morphogenic field

In the next experiment let the CA interact with the obstacle. When it dies do not replant a zygote. Watch the x indicator in the applet as it approaches the obstacle (x = 15).  Suddenly the CA is “reincarnated” lives for a while and dies. Actually when the CA dies, its ghost, which is a vector with zeroes, continues circulating and eventually interacts with the obstacle. Although the field is empty from cells, it remembers how to react.

Further reading: Creativity