Introduction
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Who has had a chance, for professional purposes or for delight, to design a model in order to organize a graphical pattern, surely has noticed that the intellectual rules and mechanisms that regulate this process are usually always the same.

That is particularly true for the geometric models, that are simpler to codify and to represent, and that are more often used in graphic design.

If, for instance, a group of persons is asked to design a simple decorative element using basic geometric shapes, like a square, we will have as result a wide variety of solutions, influenced by subjective factors, that vary from person to person, but also an unquestionable constant in the logical choices that build the composition.

One of the possible results is the following:

Figure 1: Example of composition

We can figure, in a simple case like that, the rules that determined the composition and we can describe them with the following declaration:

"Compose two squares so that one is inner to the other and that the diagonal of the one inside is equal to the side of the one outside. The two figures have complementary colors".

From this description, we can observe that the compositive choices are of two types: one geometric and one chromatic. The first regards geometric elements, like dimensions and shapes,the second define the colors. So the composition can be divided in two parts, the first produces the following result:

... and the second this one:

Taking into consideration the first result, we can list one series of passages:

1. To build a square of any side-lenght
2. To divide every side of this square in two parts with a middle point
3. To build a second square inside the first square using the middle-points we assigned before.

It's easy to state that this sequence of actions produces the expected result, but we must understand that these actions require us to have the notion of the fact that connecting the middle-points of the sides of a square we can obtain a second square whos diagonal is the same lenght as a side of the first square.

An other possible chain of rules can be the following:

1. To build a square of whichever side
2. To build a square with the diagonal equal to a side of first square
3. To position the second squared inside the first square in an appropiate way

Also in this case we have obtained the same result, but as opposed to the first case, we have constructed the second square setting up a relation with the first one. Now it stays necessary to define the positioning of the second square.

Let's consider a third construction:

1. To build to a square of whichever side
2. To build another square with the diagonal equal to a side of first square
3. To find the position of the second square according to the relations given before

In this case the expected result is obtained exclusively from the formulation of logical rules between the extents taken into consideration.

All these three examples use a foundation of formal logic for the rappresentation, with various levels of inductive reasoning.

It exists, in fact, another way to obtain the result and is that one of the cartesian construction of a shape in the plan. We think that this last modality is inadequate for a logical reasoning.

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Last Modified: Wednesday, 2009-03-25 12:53 PM