Flippy Doodle: Art of Anatoly Fomenko (Анатолий Фоменко)

Anatoly Fomenko is a distinguished mathematician and a well-known specialist in the fields of geometry, Hamiltonian mechanics, calculus of variations, computer geometry and algorithmical problems in pattern recognition.

Fomenko also has a talent for expressing abstract mathematical concepts through artwork. Since the mid-1970s, Fomenko has created more than 280 graphic works. Not only have his images filled pages of some of his own books on geometry, but they have also been chosen to illustrate books on other subjects (including statistics, probability, number theory etc) by many other mathematicians. In addition, his works have found their way into the scientific and popular press and have been displayed in more than 100 exhibits in the Russia, USA, Canada, the Netherlands, India and much of Eastern Europe.

Fomenko description of his technique probably sounds unlike anything that most of us have ever previously heard or learned about drawing. He never starts with rough sketches, copies, or outlines. Rather the final drawing appears all at once as a clean copy. "Each mark is final, and my hand does not return to it again".

- via Virtual Math Museum

(click on images for larger version)

SIMPLICIAL SPACES, CELLULAR SPACES, CRYSTAL AND LIQUID

India ink and pencil on paper, 43 x 61.5 cm.

The theme of this image is cellular spaces, which figure largely in the field of topology and can be formed easily by gluing together elementary bricks. The mental picture of a cell complex is of something pliable, soft, amorphous, flexible, and even animated – something like a deformed clay sculpture. In the image’s upper right-hand corner, an enormous, strange crystal is evolving, one with a complicated symmetry group. Indeed, a branch of group theory is the classification of crystal structures, and in this case we can clearly see just how complicated the intrinsic symmetry of a crystal lattice can be. (Virtual Math Museum)

THE APOCALIPSE (REVELATION)

India ink and pencil on paper, 48 x 69 cm.

Figures are strewn about in various stages of transformations. Objects – a radio, a teapot, a chessboard – have been cast around in the clutter. Even some mathematical ideas come onto play, such as notions of infinity. Deformations of human figures call forth the idea of homotopy and homeomorphisms. Even the clouds in the sky recall fractal images. (Virtual Math Museum)

THE TEMPTATION OF ST. ANTHONY

India ink and pencil on paper, 61 X 85 cm.

A great two-headed monkey races over the horizon beside a figure on horseback who is carrying a scepter and galloping over a sea of drums. To the left, side by side in a long line, figures sound their trumpets into the sky, while below another figure plays a keyboard. Seated on stereo equipment, yet another figure read a mathematics notebook while the central figure puzzles over the entire setting and smokes a cigarette. In a sense, this image was inspired by the medieval legend of the temptation of St. Anthony, combined with certain mathematical ideas and images. For instance, the trumpets in the upper left are based on funnel-shaped surfaces on which a hyperbolic metric is realized. (Virtual Math Museum)

DEFORMATION OF THE RIEMANN SURFACE OF AN ALGEBRAIC FUNCTION

India ink on paper, 44 x 62 cm.

The model shows a deformation of a Riemann surface of a special algebraic function, set in four-dimensional Euclidean space.

HORNED SPHERE

Depicts an object that is well known in the three-dimensional topology. Clearly demonstrates one of the important facts in the theory of embeddings of two-dimensional surfaces in three-dimensional Euclidean space. It is well known that if two-sphere smoothly embedded in three-dimensional Euclidean space (ie non-self is embedded as a smooth surface), it divides the space into two open domains. One of them is homeomorphic to a three-dimensional ball, and another - the complement of this ball in space. Both these regions are simply connected. This means that any continuous closed path (ie a loop), which lies in an area continuously contracted to a point on it. (Fomenko Graphics)

DIMENSIONAL SURFACES IN THREE-DIMENSIONAL SPACE

On the right are visible areas; on the left, like the leaves of giant ferns, grow projective plane. In the foreground - the Möbius strip, in the form of crosscap. You get something like a sea animal. It is easy to see that crosscap actually represents a Mobius strip. It is located in space so that its border is a flat circle. Projective plane is obtained by gluing a disk with a Mobius strip along their common border. Therefore, the "fern" is associated with both a Mobius strip, and with the projective plane. (Fomenko Graphics)