Success in the Real World

In the known real world the success of a system is dependent on his ability to intake enough energy

to compensate for the consumption of energy in a 'sufficient' manner. Additionally there should be some offspring to compensate for the finite duration of a system $g' \in G'$ . Thus we have the condition that $consume(e,t,t') \leq intake(e,t,t')$ and $\vert OFFSPRING(g',t,t')\vert > 0$ ^5.3. Thus there are some 'real' parameters which constrain the success of a real system.

In a simulated world one has to provide such constraining parameters in some analogous way.

Therefore the world

as the world of the working population

as well as every element (= system) $g' \in G'$ provides a basic mechanism for energy intake, energy consumption, offspring generation as well as process termination.

Based on this minimal framework of operations one can observe the success or failure of a working population

only by 'counting' the number of offspring as a 'hint' for the 'quality' of the working system.

Here it is helpful to distinguish between the 'genotype' and the 'phenotype' of a system. Real systems occur in two different modes. While the genotype $g' \in G'$ gives only the 'instructions' (the 'blueprint') for the phenotype $pg' \in PG'$ of a system, the phenotype does the observable work in the real world. Thus a phenotype

represents a system which has some input from the world

as well as it can have some output. The transition from the genotype to the phenotype is realized by some growth-function $growth: G' \longmapsto PG'$ . Thus we have:

$\displaystyle ENV$	$\displaystyle \subseteq$	$\displaystyle POS \times PROP$	(5.22)
$\displaystyle POS$	$\displaystyle \in$	$\displaystyle 2^{X \times Y \times Z}$	(5.23)
$\displaystyle PROP$	$\displaystyle =$	$\displaystyle O \cup G' \cup PG'$	(5.24)
$\displaystyle change$	$\displaystyle :$	$\displaystyle ENV \longmapsto ENV$	(5.25)
$\displaystyle intake$	$\displaystyle :$	$\displaystyle O \times PG' \times DUR \longmapsto E^{PG'}$	(5.26)
$\displaystyle consume$	$\displaystyle :$	$\displaystyle PG' \times E_{PG'} \times DUR \longmapsto E_{PG'}$	(5.27)
$\displaystyle move$	$\displaystyle :$	$\displaystyle PG' \times ENV \longmapsto ENV$	(5.28)
$\displaystyle DUR$	$\displaystyle =$	$\displaystyle TIME \times TIME$	(5.29)
$\displaystyle create$	$\displaystyle :$	$\displaystyle PG' \times PG' \longmapsto PG' \times PG' \times G'$	(5.30)
$\displaystyle growth$	$\displaystyle :$	$\displaystyle G' \longmapsto PG'$	(5.31)
$\displaystyle LIFESPAN$	$\displaystyle =$	$\displaystyle DUR$	(5.32)
$\displaystyle death1$	$\displaystyle :$	$\displaystyle PG' \times LIFESPAN \times CLCK\longmapsto \emptyset$	(5.33)
$\displaystyle death2$	$\displaystyle :$	$\displaystyle PG' \times E \longmapsto \emptyset$	(5.34)
$\displaystyle PG(x)$	$\displaystyle iff$	$\displaystyle \langle E,G', consume, IntakeArea, MoveArea>\rangle$	(5.35)
$\displaystyle IntakteArea$	$\displaystyle \in$	$\displaystyle NAT$	(5.36)
$\displaystyle MoveArea$	$\displaystyle \in$	$\displaystyle NAT$	(5.37)
$\displaystyle W(x)$	$\displaystyle iff$	$\displaystyle \langle ENV, O, G', PG', growth, intake, create, move, eval1, death1, death2, change \rangle$	(5.38)
$\displaystyle eval1$	$\displaystyle =$	$\displaystyle offspring$	(5.39)
$\displaystyle offspring$	$\displaystyle :$	$\displaystyle 2^{PG' \times PG' \times G'} \times DUR \longmapsto NAT$	(5.40)

Thus a world

consists of an environment

with properties

located at positions

. A position can be a set of vectors

. The distribution of properties at positions can change

. Properties can be objects

, working genotypes

as well as phenotypes

. With the function

one can generate phenotypes

out of genotypes. The function

can enable a working phenotype

to transfer objects, which have been 'picked up' from the 'intake area', into energy

. A phenotype can be moved

within the distance of MoveArea. Two phenotypes can create a new working genotype by

if they are 'close enough'. There is also a death-function

which deletes a working system if the lifespan has been ended. If within the 'normal' lifespan the energy drops below zero a death will also happen with

. The function

computes for every set of indexed genes and phenotypes for some duration a number $n \in NAT$ as 'fitness value'. The values of the eval()-function obey an ordering.