Two kinds of attractors

The CA is controlled by the following buttons:
Shorter: Makes CA shorter.
Longer: Makes CA longer.
Plant CA: CA is planted.

The obstacle is controlled by the following buttons:
Upward: Moves obstacle upward. Its y-coordinate is displayed as ycoord =.
Downward: Moves obstacle downward. Its y-coordinate is displayed as ycoord =.

Resources= the amount of resources the CA has.
ycoord= The y-coordinate of the obstacle

When the experiment starts, a zygote is planted at  the bottom line. The CA starts moving upward  and its resources decline.  It approaches the obstacle which acts as a “filling station”  since it supplies the CA with resources. The CA  oscillates around the obstacle and does not to cling to it. It continues upward before replenishing all its resources. Only on its way back it clings to the obstacle until its resources were replenished. From then and on , whenever the CA meets the obstacle it clings to it until its resources are replenished.  

Now click on ‘longer’ and observe the CA and its history. Following this experiment you may  change ycoord, then plant a CA and watch what happens

Please observe the following:

1. Maturation: After the zygote is planted the CA matures and elongates while moving upward. When mature  it oscillates around its center of mass and repeats its oscillation after a certain period.
2. Memory: The CA remembers where it was heading before meeting the obstacles and continues in the same direction after leaving it.
3. The obstacle is a zygote which is formed and killed at every time step. When interacting with the CA it is incorporated into it.
4. Structural attractor: When moving, the CA oscillates around its center of mass, and repeats its oscillation after a certain period. In order to see its structure click on ‘Longer’ which displays the CA history.
5. Perturbation:  Interaction with the obstacle initiates a perturbation during which   the CA acquires a new structure. It is perturbed also when  leaving the obstacle whereupon it regains its original structure.  
6. We may distinguish between two attractor types:
6.1  Structural attractor manifested by   repeating CA oscillations.
6.2  Positional attractor when the CA interacts with the obstacle and stops moving.
7. Structural attractor is called also  CA solution.  It is closely related to the notion of  a steady state, or equilibrium. As the CA moves it maintains a solution, and when perturbed it  creates a new one, like when meeting the obstacle, otherwise it may die.

Now regard the system as a whole. It too occupies an attractor which is traced by the black line and CA structure.  In other words the system   state is defined by two coordinates {CA structure, CA position}