The connection between mathematics and art goes back thousands of years. Mathematics has been used in the design of Gothic cathedrals, Rose windows, oriental rugs, mosaics and tilings. Geometric forms were fundamental to the cubists and many abstract expressionists, and award-winning sculptors have used topology as the basis for their pieces. Dutch artist M.C. Escher represented infinity, Möbius bands, tessellations, deformations, reflections, Platonic solids, spirals, symmetry, and the hyperbolic plane in his works.

Mathematicians and artists continue to create stunning works in all media and to explore the visualization of mathematics--origami, computer-generated landscapes, tesselations, fractals, anamorphic art, and more.

Jean-Francois Colonna :: A Gateway Between Art and Science

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"Clover-52," by Jean-Francois Colonna (Centre de Mathematiques Appliquees, Ecole Polytechnique)This image shows the lack of associativity for addition and multiplication inside a computer. In order to be able to obtain the exact same results over the years for a certain computation, I did include the definition of some "devices" in my own programming language, which allow the definition of the precise order of the arithmetic operations: +, -, *, and / (by the way, parentheses won't do that, for example, X=A+(B+C) does not mean T=B+C then X=A+T).

This opens the door to something very powerful: The possibility to dynamically redefine the arithmetic used when launching a program. This picture and "Clover-51" are the results of the combination of eight elementary pictures: 3-clover, 4-clover, ... ,10-clover with substitutions like (A+B) --> MAX (A,B), (A*B) --> (A+B).

"Clover-51," by Jean-Francois Colonna (Centre de Mathematiques Appliquees, Ecole Polytechnique)This image shows the lack of associativity for addition and multiplication inside a computer. In order to be able to obtain the exact same results over the years for a certain computation, I did include the definition of some "devices" in my own programming language, which allow the definition of the precise order of the arithmetic operations: +, -, *, and / (by the way, parentheses won't do that, for example, X=A+(B+C) does not mean T=B+C then X=A+T).

This opens the door to something very powerful: The possibility to dynamically redefine the arithmetic used when launching a program. This picture and "Clover-52" are the results of the combination of eight elementary pictures: 3-clover, 4-clover, ... ,10-clover with substitutions like (A+B) --> MAX (A,B), (A*B) --> (A+B).

"Artistic View of a Bidimensional Texture," by Jean-Francois Colonna (Centre de Mathematiques Appliquees, Ecole Polytechnique)This image was obtained by means of a self-transformation of a fractal process.

"Bidimensional Visualization of the Verhulst Dynamics," by Jean-Francois Colonna (Centre de Mathematiques Appliquees, Ecole Polytechnique)In this image, grey, orange, and red represent negative Lyapunov exponents; yellow, green, and blue represent positive Lyapunov exponents. The two groups of colors distinguish stable systems from chaotic ones.

"Artistic View of the Klein Bottle," by Jean-Francois Colonna (Centre de Mathematiques Appliquees, Ecole Polytechnique)In mathematics, the Klein Bottle is a non-orientable surface, i.e. a surface with no distinct "inner" or "outer" sides. Other related non-orientable objects include the Mobius strip and the real projective plane. Whereas a Mobius strip is a two-dimensional object with one side and one edge, a Klein bottle is a three-dimensional object with one side and no edges.

"Doubly Impossible Staircase," by Jean-Francois Colonna (Centre de Mathematiques Appliquees, Ecole Polytechnique)Traversing along the outside, the stairs always rise; but traversing along the inside, they always descend. Finally, alternating between the exterior and interior, it behaves like a normal staircase. -- Jean-Francois Colonna