Esnuka not only helps learning games of billiards, pool and snooker but also has computer learning games of evolution with his options of simulation of evolution Esnuka-I, II and III.

On top, Esnuka has a simulation of evolution of the billiards balls using the GTCEL genetic algorithms and Mendel's laws.

To some extend, it is believed that genetic algorithms have proven the theory of Darwin but, obviously, it is not like that. In fact, it could be just the opposite because the genetics algorithms are maths functions to search new situations with different approaching methods.

There ise always the need for a goal or a math function to optimize within the genetic algorithms and that is closer to a teleological or finalist evolution than a Darwinian evolution.

Furthermore, as the genetic algorithms have been design by humans, they are always the result of an intelligent design.

Nevertheless, even in the case some genetic algorithms could be considered as consistent with the theory of evolution of natural selection, it is clear that they do not prove that theory and that there can be non-Darwinian genetic algorithms.

Here is the description of a specific option designed to show a fast evolution without needing to play billiards, making easier to understand the rules behind the computer learning games of evolution.

Again, it may resemble too difficult to understand the way evolution takes place in these computer learning games, but even in the case one does not understand the rules of the theory of evolution, it will be assimilated their effect intuitively.

Of course is advisable to read the GTCEL but it is not necessary, in fact the idea o learning while discovering the games in the computer is not a bad option.

This option of Esnuka allows the observation of the changes produced by a specific number of generations for the whole population, for 20, 30 or 100 individuals. If Sound is off it will be set to 100.

The difficulty level parameter controls the way to calculate the potential of genes. For difficulty levels 1 and 2 the initial values of the potential of the genes are randomly calculated within a limit of 1 to 3 and are independent from each other. Otherwise, for values 3 and 4 the potential of the genes of an individual is equal. This characteristic hardly affects the evolutionary process, however in the latter case, the values tend to be less extreme within their range.

This option appears on the screen with two different or equal sized circles respectively. Nevertheless, if the colour inversion function is activated, all the genes will be set up with the same value and this is shown on the screen by one circle.

The difficulty level parameter is also used to decide which simulation rules of the genetic algorithms to use in accordance with either Esnuka I for values 1 and 3 or Esnuka II for values 2 and 4.This is represented by one or two vertical lines on the screen.

Simulation of evolution Parameters configuration
Esnuka - the option of evolution simultion

When simulation is requested, a screen will appear displaying a randomly calculated initial situation within a limit of 1 to 5; in other words, the left-hand side of the evolution screen. The balls will depend on the configuration of the fixed verification and complementary genetic algorithms parameters.

Every time a key is pressed, a new generation will be calculated according to the parameters established in the configuration menu. These parameters are constantly displayed on the screen.

Simulation of evolution Initial situation
Esnuka - the option of evolution simultion

The detail of each individual evolutionary step is identical to the one used in Esnuka I and II, the rules governing the interchange of genes are Mendel's established theories and the probabilities of transmission are equal for each gene.

In this way, the effect on evolution of Logical Verification of Information and complementary characters concepts can be seen.

Simulation fractals
Fractals in the option of the simulation of the evolution.     Fractals in the option of the simulation of the evolution.

In particular, the selection of external verification means that the figures resemble the tip of an arrow; if complementary genes are added the figure slightly changes its shape, to remind us on occasion of fractals.

The speed of evolution depends on its parameters and is the same with or without external verification; nevertheless the former case will be out of step compared with the latter.

Another visible effect is the increase in distance between individuals when internal evolution parameters are small compared to external evolution parameters and vice versa.

Simulation fractals
Fractals in the option of the simulation of the evolution.     Fractals in the option of the simulation of the evolution.

By fixing very small endogenous and exogenous evolutionary parameters we can study the behaviour of evolution in the long term, this is equivalent to increasing dimensions of the evolutionary window without changing the evolutionary parameters.

Differences between consecutive colours are always constant and endogenous and exogenous evolutionary parameters are expressed in percentages.

As an additional explanation, we could say that colours are always standardised in the scale 1 to 20, therefore, the potential represented by colours is the same in the cases of genes, characters and individuals, the only exception being individuals with complementary characters. For example, the potential of an individual with two complementary characters with potential equal to 10 will be 10 times 10 = 100, divided by 20 = 5, to standardise the range 1 to 400.

Finally, I would like to say that computer learning games help to understand things but complex ideas will need certain time, its life...