Flowing Transformations

This web page displays a continuous series of curve transformations from their linear origins with a very structured flow of color.

The display consists for three parts: first the presentation of the faded original curve, then the transformation in a flowing manner, and finally the spine of the transformed curve to reinforce the path it traveled through.

All of the curves are computed and drawn in real time, randomly selected from a gallery of over 300 possible curves.  Each is based on a graphic interpretation of a simple spirolateral curve, then transformed according to one of the following methods: antiMercator, circular, circle inversion, harmonic mean inversion, hypocycloid, epicycloid, epitrochoid, piriform, bicorn, tear drop, lips, lame, or hippopede curve.

Individual images in this series can be found at: www.netcom.com/~bitart

Algorithmic generators and transformations are used to develop a series of images that explore the unexpected from the very simple.  These images, that at one time elicit fragments of a far off  future, at the same time remind me of past ritual icons and symbols.  The starting linear and resulting circular forms remind me of the past while the lack of color and the sharp edges envision a possible future. 

The series of images included are part of a larger series investigating the formation of artwork using basic mathematical concepts.  This series is based on a mathematical figure called a "spirolateral".  It is simply a square spiral with increasing length of turns and the turns repeating themselves.  The turns can be all in one direction or certain turns can go the opposite direction.  The most interesting of these are ones that close on themselves, not all do.  Investigating a series of possible turning angles, number of turns, number of  repeats, and trying all revered turns,  over 10,000 spirolaterals have been identified that are closed.