
Linear patterns in geometrical space of circles.
Multicolored lines form volumetric pictures of phantom visual images.
Geometrical pattern in space of the transformed circle.
Pattern crossings of lines in geometrical figures of squares. 
If to divide a visible plane of space by means of shapes of
geometrical figures and outlines of polygons, and also if to connect
corners of polygons and points on sides of figures then crossings of
connecting lines form geometrical linear patterns or otherwise to tell
phantom networks. At the left it is possible to see linear patterns constructed within
the circles. Namely each circle is divided into three parts and each
third is divided into 9, 8, 7, 6 parts. Points of divisions are
connected by lines which in space of circles form various patterns or
otherwise to tell different phantom images of geometrical figures
depending on numbers of points which divide third parts of each circle. The shown images display only some linear patterns, but actually in
view of mathematics there is a much greater variety of similar phantom
networks. The shown linear patterns or otherwise to tell geometrical phantom
networks are computer art graphics, namely images are drawn by means of
software programs for visual work with digital pictures on screens of
computers.  Linear patterns and phantom networks in seventeen online galleries of this website are drawn with color felttip pens and paint markers on paper sheets unlike computer graphic images on this page. Namely patterns in galleries are drawn on a paper by means of writing tools as a basis of real graphic drawings and geometrical pictures in a context of fine arts, but however I do not deny an opportunity of computer visualization and creation of digital pictures by means of multimedia technologies. I consider the shown graphic drawings in galleries as phantom
fantastic networks or linear textures, or otherwise to tell patterns of
geometrical figures in which there are
phantoms of imagination and pictures of mental images. The visible validity is a flat projection of the world because
perspectives of space are perceived by eyesight, and neural cells in a
retina of eyes have a flat surface. It is possible to tell that eyes
perceive perspectives of volumetric space, but our brain builds the
image of visible validity on a flat surface of retina by means of
squares, circles, triangles or other geometrical figures the same as any
drawings or plans, or geodetic maps are under construction in human
ideas. And consciousness in visual zone of a brain carry out geometrical
transformations of visual sensations, and people create volumetric
pictures of the world.  Our eyesight and consciousness perceives elementary figures of
geometry, but surrounding space includes latent geometrical contents
which we do not realize as it is not obvious for eyes. Namely there are
more complex figures which are inaccessible to human understanding, but
however if to understand laws of geometry it is possible to realize
psychophysical principles according to which our brain calculates mental
images of the global validity. And also it is possible to see
multivariate linear patterns which exist in complex geometry of visible
world. Global validity is constructed according to mathematical principles of symmetry and proportions. We are surrounded with grandiose geometry of space in which harmony of lines and systematic outlines of diverse world objects have expansion, but we can see and realize geometry of surrounding shapes if eyesight divides visible measurements of the world, and then contours of global validity become obvious. Many concepts of space have been investigated and formulated, or
designated by images in pictures of artists or painters who marked in
ideas a strict geometrical essence of spatial perspectives, and who saw
exact mathematical proportions in structure of the created world.
Strange geometrical objects in art compositions of Kandinski or abstract
geometrical figures in pictures of Malevich, and also spatial forms of
many other abstract artists are attempts to see geometry of the world,
but nobody can measure all world finally. It is possible to argue on visual harmony or disharmony, and also
about proportions and disproportions in abstract pictures or graphic
drawings, or other art works, but in essence any rules of the fine arts
and criteria of beauty of geometrical forms or shapes, and in particular
principles of beauty in pictorial figures of human bodies are identical
to universal laws of world space which have exact parameters. Namely
global spatial harmonies can be measured and calculated, and also can be
proved in view of scientific geometry. 
Content of this page in the future will be increased, as the theme about
patterns of geometrical figures in a context of the fine arts is very extensive.
If you have own notions about geometry of space and geometrical patterns of
world around, and your ideas can be really represented, then your
representations can be shown in a context of online of gallery on pages of this
website, or I can give links to websites of your
images in the global network of Internet.