Academic Open Internet Journal
ISSN 1311-4360

Volume 17, 2006

MATHEMATICAL ANALYTICS IN FASHION COMPOSITION

Dr. Assoc. Prof. Penka Popska, Engineering department-Fashion & Textile design, Technical University-Sofia, Bulgaria

Textile Artist – Marina Popska

The relations between two elements in the composition may be considered as two aspects – as a type and as a class of the relations.

The classes’ relations. The relations between the composition’s elements are treated according to the definitely conditionally separated signs (for example: size, colour, configuration etc.) In this case the compared elements will be named differential elements. The separating signs belong to certain class signs but within the limits of every class may separate various signs and their gradation.

Types of relations. The elements of composition may be considered each in relation to other as different or identical (relation type - identity) as different what can be fixed quantitatively (relation type of difference) and in qualitative aspect what is not reduced to the level of quantitative characteristic (relation type - contrast).

The information may be considered as a behavior of the variety through types and classes’ relations.

The information as a combination of differences and identities.

The compositions a and b from figure 1 may be described as a behavior of variety between the elements by class of signs (elements’ size) by means of relation identity.

The relevant quantity information may be expressed as following:

J = log₂_,

Where: N – a number of positions covered by the elements;

n₁ – the number of elements from the first type;

n₂ – the number of elements from the second type;

n₃ – the number of elements from the third type;

n_k – the number of elements from the k_th type.

In the present case the intuitive presentment for the level of the variety in composition a and b coincide with the quantitative definition of the information.

For a: J = log₂ = log₂30 = 4,91 bits

For b: J = log₂ = log₂60 = 5,91 bits

Respectively J_a – J_b = 1 bit (bit – a unit of information)

In a complicated case – Figure 2.

Figure 2

Now the elements in the compositions a and b are not different by one sign already. We can divide them by three:

1) By configurations;

2) By area of the elements;

3) By colour (achromatic).

The quantities of information for one unit composition will be:

for a: J = log₂ ≈ 8,49 bits

for b: J = log₂ ≈ 5,91 bits

Respectively: J_a – J_b = 2,58 bits.

To see the full illustration of the allocation of the variety it may be expressed by information as a combination of different and identical differential elements of the composition.

To determinate the quantity of the information in the quoted examples we do not took the mutual position of the elements regardless of the fact that the identical distances between them decrease the common variety and in the same time the accident of the elements’ dispensation as non repetitious increases this variety.

At the same time such kind of variety may be expressed as a quantity of the information taken by different and identical distances between the elements. In this case the background that the elements are located on is considered as adequate from conditionally separated differential elements.

The information as a combination from level of difference.

The most complicated behavior of the variety is based on the allocation of difference between the elements’ level but not on the allocation of different and identical elements. To explain this we will give a simple example. On figure 3 are shown two composition the elements each of them are different within the limits of their composition.

Figure 3

The quantity of information respectively taken by the relation of the identity will be equal to:

J_a = J_b = log₂ ≈ 4,58 bits

In this case it obviously does not correspond to the behavior of the variety because the composition on figure 3 a is more varied from the composition on figure 3 b which is built on a proportional system (a/b = b/c = c/d).

To characterize adequately the variety of the quality information it is necessary to accept the quantity different and identical levels of difference between the elements for basis. In this case the differences exhaust class 1 signs. If the level of difference between two elements is marked with S for the composition on figure 3 a and b the quantity of the identical levels of difference will be allocated in the following way:

For a: N = 6; n₁ = 3; n₂ = 2; n₃ = 1

As:

S_1-2 = S_2-2 = S_2-3 ≠ S_1-3 ≠ S_1-4; S_1-3 = S_2-4 ≠ S_1-4

Where: N is the total quantity of the separating level of difference;

n₁, n₂, n₃ – quantity of the separating levels of difference respectively to 1^st, 2^nd and 3rd type.

For b: N = 6, N_1-6 = 1

The information quantities will be:

For a: J = log₂ ≈ 5,91 bits

For b: J = log₂ ≈ 9,49 bits.

The composition a contains less information than composition b (J_a – J_b = 3,58 bits) which in this case corresponds with the ideas of variety.

The continuity of the spatial disposal of the elements of the composition – lines, outlines, forms – sets up a display of relations of preceding the totality which also may be definite according to the quantity of the information of that type relations.

In the complicated compositions the information is allocated in a different way – not only between the separate spatial elements of the composition but also between the differentiated levels of the composition, i.e. between its parts as a whole.

To illustrate such presentment one should examine the simplest examples of meter and rhythm combination. (Figure 4).

A, B, C and A₁, B₁, C₁ may be examine as elements. In that case:

For a: J = log₂ = 0, because n₁ = n₂ = n₃

For b: J = log₂ = 1,59 bits

In case of separation the next level as elements may be presented a, b, c and d. The quantity of information for each part will be:

For a: J = log₂ ≈ 4,58 bits

For b: J = log₂ ≈ 0

The total quantity of information between the levels will be:

For a: J = 4,58 bits; For b: J = 1,59 bits.

Fashion is, by its very nature, an ever-changing art.
It is this continual evolution, the constant reinvention of old trends and the creation of new ones that lends the fashion industry its excitement and glamour. Figure 5.

Fashion composition can be analyzed by the view of placing the appropriate elements and arranging them with combining the different parts of the clothes. None of the fashion clothes are made just like that, throwing together objects or filling the details without an idea how is going to look like as a final result. Fashion designers develop a whole range of related ideas to produce groups of garments that work as a collection. A consistent approach to import factors such as color, shape, pattern, and proportion helps to create the best composition for each cloth.

Figure 5

LITERATURE

1.Popska .P Dizain na oblekloto (TU-Sofia-1999.)

2.Popska.P Dizain na tekstil I obleklo (Tehnika Sofia –2000.)

3.Bernstein M., Die Schoheitder der Farbe in der Kuns und eber tglichen Leben, Munshen, Deiphin,

1925-152.

4. Color Tagnus- Burichtt von der TATC (Association unternationale le lacouleur) Tagung. Stockholm, June,9-13,1969.

5. DANGER E.mc P, Usingcolour tossel, Paress,1968-224 p.22.

6. EBBING House A., Theorie die Farbensehens, Leipzing, vose 1893.

7. Dolapchieva G., Geometrical principles for designing ladies^,underwear, Tekstil I obleklo 10 /2001"

Technical College - Bourgas,