Jean Constant
Mathematics represents the expression of abstract intelligence at its best. It is the fertile ground that inspires me to celebrate both our collective intellectual achievement and the dynamic of its association with our more tangible environment.
The development of computer-based mathematical visualization programs such as Dr Palais' 3D-XplorMath software have been an inspiration and a distinct incentive that encouraged me to develop further my interest in this field.
Breather & soliton extracted from Dr Palais's 3D-XplorMath mathematical visualization software.
Solitons are very stable solitary waves. When they are located mutually far apart, each of them is approximately a traveling wave with constant shape and velocity. The term breather originates from the characteristic that most breathers are localized in space and oscillate (breathe) in time. The image is built like a visualization of a musical composition: breather orchestra in the background repeating a sustaining theme, breather spheres surging forward to emphasize the theme in targeted sequences and one-soliton solo intervention sprinkled through the performance. The spectator will determine what instrument should each soliton be.
(Tools: 3D-XplorMath, Adobe CS5, Pixologic-ZBrush)
Breather & soliton figure variation.
Pseudo-spherical Surfaces are being the object of much investigation in the field of music. A breather is a nonlinear wave in which energy concentrates in a localized and oscillatory fashion. Soliton suggests solitary waves that behave like particles. The close relationship between mathematics and music inspired me to create a container for future musical works relating to the soliton and taken after leather bound musical "coffrets" of the court of France in the XVII centruy - as collaboration between the arts was flourishing.
(Tools: 3D-XplorMath, Adobe CS5, Pixologic-ZBrush)
Two soliton & Four soliton figures.
In mathematics and physics, a soliton is a self-reinforcing solitary wave. Solitons arise as the solutions of a widespread class of weakly nonlinear dispersive partial differential equations describing physical systems. Their characteristics are to be of permanent form and localized within a region. They can interact with other solitons, and emerge from the collision unchanged (Kanehisa Takasaki - Kyoto University).
The purpose of this image was to put highly abstract concepts in the perspective of a broader esthetic and cultural environment. The title & composition is a reference to XVIII & XIX century paintings of artists' "ateliers" (David, Delacroix, etc...)
(Tools: 3D-XplorMath, Adobe CS5, Pixologic-ZBrush)