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If to divide a seen plane of space by means of forms of geometrical
figures, and also if to divide the sides of figures and to connect
points of divisions by lines then crossings of lines form geometrical
patterns.
A variety of patterns can be indefinitely big as if to change
mathematical parameters of divisions then shapes of patterns changes,
and as a result it is possible to see that in geometrical crossings of
lines there are universal laws according to which patterns vary.
If we delimit and divide geometrical figure’s contour and link points
of division with line interceptions geometrical patterns can appear as
the result. These patterns’ view varies miscellaneously when division
parameters are changed.
At the left it is possible to see patterns constructed within the
circles. Namely each circle is divided into three parts and each third
part is divided into 9, 8, 7, 6 parts. Points of divisions are connected
by lines which form different patterns depending on numbers of
divisions.
Also it is possible to see the circle in which lines of a pattern have
different color, and it is possible to see a pattern which is formed in
a field of the transformed circle.
Below it is possible to see two squares which too have different pattern
crossings of lines depending on divisions of sides into 8 or 7 parts.
The shown images show only some patterns, but actually there is a much
greater variety of such patterns.
Surprising pattern crossings of lines exist in a field of hexagons or
heptagons.
In essence patterns can be constructed in contours of different
geometrical figures, and also special geometrical figures and parameters
of divisions can be calculated for formation of very diverse patterns.
These patterns may be created not only in usual contours but in
unusual contours too. The side divisions, which are necessary for some
special patterns’ creation, may be received as result of special
calculations.
The shown patterns are computer graphic arts, namely are executed by
means of the graphic computer program.
Unfortunately known computer programs are intended for the decision of
the general geometrical tasks and consequently can not be used for
drawing the shown patterns. That is known computer programs are too
complex that allows to draw patterns by means of difficult operations,
but it is necessary to make the special computer program which has a
simple set of functions and in essence is the game program which allows
to design desirable geometrical constructions and to carry out necessary
geometrical transformations which suppose creation of every possible
patterns.
Then any interested user of such game or entertaining computer program
can draw patterns, and can investigate aspects of geometry which can be
seen in lines of patterns.
To view true variety of patterns it is necessary
some program equipped with special set of tools, which allow, with help
of some key operations, to construct desired geometrical composition, to
use color and to accomplish necessary conversions. And in this case
everybody can research multi-sided interesting aspects of this type
geometry.
I draw patterns on a paper by means of a ruler and felt-tip pens as I
use patterns as a basis of the future images (graphic drawings), but
nevertheless I do not deny an opportunity of computer visualization.
I consider patterns as phantom (fantastic) networks or linear textures
in which there are every possible images (phantoms).
If the sight looks a little further or nearer a plane of the image then
lines of patterns seem as abstract distances which are compressed or
stretched, and form hypothetical intervals as if refract in multivariate
space. Also it seems that in seen geometrical structures there are
outlines of supernatural forms or phantoms which is diverse change and
turn to comprehended objects of perception.
Pattern lines create something like refractions in multidimensional
space and it seems us that supernatural forms bleed through and obtain
specific outlines.
The seen validity is a flat projection of the world as it is
perceived by an eye retina which has a flat surface. It is possible to
tell that eyes perceive space but eyes build an image of the world on a
flat surface of a retina of eyes by means of squares, circles, triangles
or other figures the same as the artist builds any drawing. And the
consciousness carries out geometrical transformations of visual
sensations and creates a volumetric picture of the world.
Our consciousness executes geometrical transformations of phose
(visual sensation) and constructs environmental world image which
consist of squares, circles, triangles and other figures.
Our sight and consciousness perceives elementary figures of geometry,
but in environmental space there is a latent geometrical contents which
we do not realize as this contents is not obvious. Namely there are more
complex figures which are inaccessible to our understanding, but
nevertheless if to comprehend laws of geometry then it is possible to
realize principles according to which the brain calculates the image of
environmental validity, and it is possible to see geometrical patterns
which exist in complex geometry of world around.
Any space structure includes closed geometrical content which does
not apparently but determines many laws of human perception.
Harmony of the world is constructed according to mathematical
principles of symmetry and proportions. We are surrounded with grandiose
geometry of space in which systematic outlines of world objects open.
But it is possible to see and realize geometry of environmental forms if
to measure a seen measure of world space by means of a sight, and then
contours of the validity become obvious.
Many concepts of space were investigated and formulated, or only are
marked in ideas of artists which saw strict geometrical essence in
structure of the created world. Strange geometrical objects of Kandinski
or Malevich, and also geometrical objects of many other abstract artists
are attempts to see geometry of the world, but nevertheless nobody has
measured and can not measure the world finally.
And also geometrical patterns of phantom images on pages of this site
are research only some aspects of world geometry.
Global culture comprehends environmental world geometrical image
miscellaneously. This image of the world is a subject of investigation for many works
of art.
It is possible to argue on harmony or disharmony, and also about
proportions and disproportions of those or other abstract pictures or
drawings, but in essence laws of the fine arts and criteria of beauty
are identical to universal laws of the world and consequently have exact
parameters, that is can be calculated and proved from the view point of
a science of geometry.
Including there can be disputable shown phantom images, but nevertheless
compositions of geometrical figures and harmonious ratio of lines form
correct proportions of patterns that makes the integral essence of
phantom images.
The main “Phantom images” concept is the fact that geometrical patterns
are integrated part of this drawings’ essence, in which environmental
world image is reflected.
This page content will be enlarged during future periods because this
topic of geometrical patterns is very wide.
If you have own representations about geometry of space and geometrical
patterns of world around, and these representations can be really
represented, then can be shown in a context of my gallery on pages of
this site, or I can give links to a site of your images in the world
network of internet. |
