A contour can be considered as an infinite number of points To manage this number (by some cognitive process e.g. a living creature or a machine with a program) it has to be reduce some way. A creative principle is needed.
This paper demonstrates such a principle by means of examples.
In short: this principle is based on a limited number of structures and operations which make possible:
-the transformation of a structure into another structure
-the differentiation of a structure
-the expansion of a structure
Three process-situations are connected with these operations:
- -the situation, after a transformation took place, is called: a hypothetical state (or expectancy). This means this state has to be tested. The outcome of the test can be:
In this case after a confirmation an expansion can follow: after a denial the hypothetical state has to be abandoned and the process should return to the structure on which the
- -denial (negation)
transformation took place, after which a differentiation can follow.
- -the situation after a differentiation is similar with a confirmed hypothetical state. In this case another differentiation or a transformation can follow.
- -an expansion can create two situations:
- -a situation in which the process cannot reach a hypothetical state. This means giving up this trial.
- -a situation in which the process reaches a hypothetical state. This state can only be confirmed in this case.
Two mechanisms of checking or control are involved:
1. internal checking: this means that spaces (every structure has its own developing space, see summary) are not allowed to overlap. Spaces may touch and the touching defines the hypothetical length of the expanding structure.
2. external checking: this means that structures are not allowed to overlap with the contour, however, when they overlap the process has to (in order to maintain the reality principle) step back to the last confirmed state.
In all the examples the contour on which the principle operates will be the same (fig. 1). It goes without saying that this choice is arbitrary so other contours could have been chosen, however, in all these cases the principle stays the same. A second choice is for 2-D examples. This is purely a matter of convenience. The 3-D working of the principle will be clear by itself. Also not of necessity is the use of a closed contour.
With respect to the approximation of the contour, two different starting-points (fig. 2 and 3) will be elaborated in the examples. This is done to demonstrate that given the different starting points the same approximation of the contour can be realized.