# Three System Laws

In my investigations on cellular automata, I came upon the following effects, which occur very frequently there and which are also responsible for the special fascination with such machines. From this, general statements can be formulated.

Context is thus the automaton theory, but the statements also have validity for other forms of optimization calculus and generally describe system behavior.

### Three System Laws of KROLL

#### (1) Emergence

(Convergence in the infinite solution space)

A system displays emergent (unexpected) behavior when it offers many or infinitely many solutions after which it is optimized.

1st system law of Kroll

#### (2) Chaos

A system shows chaotic behavior when two forces or conditions act against each other and transcend one another.

2nd system law of Kroll

#### (3) Oscillating Systems

Emergence and chaos can lead to oscillating systems.

3rd system law of Kroll

### Notes and examples:

To (1): Optimization calculations in an infinite solution space can lead to an unexpected and unpredictable system behavior. Example: Any optimization of the position of objects in the space, which does not also define an orientation to the space axes, allows an infinite number of solutions.

Example to (2): A minimization of the space with a simultaneous rule for the minimal distance of the objects leads to chaotic behavior.

To (3): Both (1) and (2) often lead - but not necessarily - to infinite system run-time, i. Both can have a destabilizing effect.

Especially when calculating the optimization, you can make use of this fact, because the system overcomes local minima. You should save the best solution so that it can be retrieved when the system oscillates between different solutions.