Output and efficiency

Resources generated at one instant (step) are called product (input).  One part of the product becomes  permanent CA structure (CA core). The other called output (CA rim) is delivered to the environment.

Product (input) = permanent structure (core) + output (rim)

The present experiment explores the relationship between core and rim. The following parameters were estimated: 1. Tolerance velocity was  estimated with regression. 2. Min[velocity] and  Max[velocity]. CA were controlled by the following functions:

delivery activation: [state[1, set point = p[1] - 0.1, state[0, k]]; {k,1,46}
delivery: [2, 1, While[p[1] > set point], 2];
delivery: [1, 2, While[p[2] > set point], 2];
change state: [state[1, i+1] = state[0, k], state[1, k]]; {k,1,46}
change state: [state[2, i+1] = state[0, k], state[2, k]];
augment state: [state[1, i+1] += state[2, i], While[p[2] > p[1]]
augment state: [state[2, i+1] += state[1, i], While[p[1] > p[2]]

CA-1 and CA-2 stimulate each other. The stimulation   was triggered by  different CA-0 states, using the change state function.    The healthiest CA-1 was triggered at  CA-0 state = 22. CA-0 state = 27 did not trigger a mutual stimulation and the CA remained isolated.  At CA-0 state = 31 the CA had the largest output  and was least healthy.

The graphs show that CA-1 velocity was the fastest, and in CA-3 it was the slowest. Nevertheless the CA-3 survived since maintaining a constant core.

The graphs depict health and output. Most CA aligned along the centeral line were isolated (like CA-2). CA-1 is the healthiest with a moderate output. CA-3 is unhealthy with a  large output.

Efficiency is defined as Max[velocity] / Min[velocity]. CA-3 is the most efficient since its core is very narrow.


Output and efficiency are negatively correlated with health. Roughly, the health ordinate is driven by velocity, and the output or efficiency ordinates, by the m-factor. However the m-factor may also accelerate velocity and improve health.

In summary:

Velocity: Accumulations of resources in the core.
Input or product: resources generated in one step. (core + rim).
Output (rim): Max[velocity] - Min[velocity] / Max[velocity]
m : Min[velocity]/Max[velocity]
Health: velocity * Min[velocity] / Max[velocity] = velocity * m
Efficiency: Max[velocity] / Min[velocity]


The isolated CA is the least differentiated. As CA interact their structure changes and they differentiate. Differentiation is controled by the m-factor, which actually controls Min[velocity] and Max[velocity]. Both may applied to measure differentiation. First let's define a CA state vector:

State[CA] = {velocity, output, efficiency).
State[CA-0] = {velocity0, output0, efficiency0}. The isolated CA-0 (stem process) serves as reference.
Differentiation[CA] = { (velocity-velocity0)^2 + (output-output0)^2 + (efficiency - efficiency0)^2} ^0.5
Differentiation[CA] normalized = Differentiation[CA] / Norm[Differentiation[CA]].