8. Observer and CA attributes

When inspecting a CA we ought to distinguish between, observer and CA attributes. In the next image a zygote was planted and the CA[600] evolves. Its history (trajectory) is outlined by the observer. It is an observer attribute. The observer plants also the zygote. The CA does not remember its history. It lives in the present (now) without any notion of the past. Nevertheless its current structure is determined by previous states, yet it does not remember them. The present state is magnified.

The next image illustrates the history of CA[600]. It is symmetric and isolated.

More information on CA[600]

7. Solution

CA histories depicted in the previous experiments are processes whose initial condition is a state containing the number 1. It is called here a zygote. You plant the zygote and the process starts evolving. Each line is a CA state at a certain moment of time. A process has three kinds of outcome:
1. Lives for ever (marked by an A in the image).
2. Dies (marked by a B in the image), or
3. Proceeds through a transient which either dies or lives for ever. (marked by a C in the image).

The study focuses on immortal processes which are called process-solutions. They are known also as attractors. We shall distinguish between regular and irregular attractors. The latter are called also strange attractors. The attractors depicted here are regular. Below is an irregular (strange) attractor.

The study explores ways which drive a process into an attractor. The experiment depicts two ways:

1. Interaction of two mortal CA ends in an immortal solution. (Second from left)
2. Interaction of a mortal and an immortal CA creates two solutions. (Last process)

Strange attractor

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6. Rule swapping

CA[rule] determines the transition from state to state. On the left a CA whose rule is 600. Up to time = 67 it grows whereupon it starts oscillating at a period of 46. The second CA [rule=357] lives only 88 days. The experiment explores how rule switching influences CA survival. At t=69 CA rule was switched from 357 to 600. After a transient period the CA settles at the CA[600] configuration which is called here a CA-solution.

At times t <= 69 rule swapping made the CA immortal. For t >69 rule swapping did not change the CA structure and it died at t=88.

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5. Interaction with a barrier

The barrier (vertical line) is made of the number 2. In the first CA history (A) the barrier was removed at day 82. The CA does not interact with it and dies on the 88^th day . Please note that the figure depicts the history of a one dimensional CA. The black line depicts the history of the barrier. At each day the barrier is placed at the same place.

In the second CA (B) the barrier was removed on day 90. The CA succeeded living somewhat longer and then died.

In the third CA (C) the barrier was removed on day 123. Initially the CA grew along the barrier, and when it was removed it regenerated and ultimately died.

During its interaction with the barrier the CA changed its structure and became a spore. This change was triggered by the barrier. Despite its new structure, the CA remembered its mature structure, which it regenerated after barrier removal.

Please note:

- The barrier represents here inert matter which is not incorporated by the CA. Nevertheless the CA uses it to remain alive and occasionally to mature and die a natural death.
- If the regenerating CA would have encountered a similar barrier, it would have continued living.
- Do you know of a modeling tool other than CA which might demonstrate a similar phenomenon?

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4. 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).
Please note:
- The chaotic CA generates non chaotic and immortal progeny (attractors).
- The CA group expands indefinitely.

The next image depicts the Lorenz attractor which does not generate non-chaotic processes. You may wonder, what is the difference between this and the previous chaotic phenomenon? Currently you lack means (tools) to distinguish between them. To me, the Lorenz attractor fails to capture (portray) chaotic phenomena of nature.



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3. Fertilization

Let’s return to the previous experiment. The planted seed is the number 1 (see chapter First Steps Oct-25). When Rule = 357 is applied to the seed it will enter its subsequent state, and so on. After some time (about 40 iterations) it will die. If you plant two seeds 22 bits apart, they will soon fuse together into one CA and become immortal and start oscillating. This simple experiment illustrates the following properties of life:

1. Fertilization
2. Emergence of a new structure.
3. Symbiosis, when the two CA fuse.
4. Their fate depends on each other.

Since if one is killed before they fuse the other will die somewhat later. Without interactiong with the other it is short lived.

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2. Interaction between two CA

The picture depicts four CA histories driven by rule #357. The first (marked by a 0), depicts a history of a single CA , which gradually grows (downward), yet will soon die. The next history depicts two CAs whose seeds were planted 5 units apart from each other. After fusing, they became immortal. The next history depicts two CAs whose seeds were 22 units apart from each other. Both grow along each other, and shortly before they die they interact (fertilize) each other and become immortal. In the last history the two CAs interact, gain mass (strength), and die.


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