Weiman – Iterated Transformations (W-IT)

… is a program (application) for interactively creating, manipulating and animating complex 3-D structures dynamically in real time.  The structures are generated by iterating simple geometric transformations hundreds of times, yielding surprisingly complex and beautiful results. 

The program is designed to be used by everyone, requiring no math nor programming on the part of the user.  Distribution is free to everyone via the web.

A session with the program is analogous to a session with a musical instrument.  Anyone can generate interesting dynamic sequences and flows of structures.   You can record any configuration by pressing the “record” button, and can save the recording in a text file of your choosing in order to continue the session or exchange it with other users.

As a visual art medium, the program generates a visual analogy of music where 3D images and their dynamic transitions play the role of notes and compositions.  The program intrinsically generates and animates many of the basic symmetry patterns of visual art including stellated polygons, spirals, helices, cornucopias, and vastly more complex forms and rhythms previously unknown.

As a mathematical tool, iteration of simple operations in one dimension yields all the finite groups; their quotient groups by factors of group order fall out as condensations in the images.  Number theory, differential geometry and many other fields are also modeled.  Many useful functions which have no closed form solution can be “solved” to approximate (discrete) levels by simply displaying the structure, which represents a trajectory of the iteration.

As a tool for physics, resonances for subatomic particles model quantum features and string theory.  Massive iterations lead to chaotic patterns which relate to phase change in Ising spin-glasses and anti-ferromagnetic materials.  Resonance and control of large degree of freedom systems are modeled.

As a biological tool, this is a model for biology rather than of biology.   At the nano scale, the program models chain molecules such as RNA and massive protein cages such as hemoglobin.  New nanomachines based on chain molecules, not gears, provide dynamic functionality for transport, keying, winding, and motility.  On a micro scale, organelles and microtubules can be modeled.  On the macro scale, tentacles, trunks and large flexible systems are modeled.

The program was written in Java3D by Carl Weiman.  Refactoring and interfaces were assisted by Doug Lyon.  Professor Lyon is also hosting the program on his website, http://www.docjava.com/, which also has many other interesting Java Webstart applications.  Please use this program freely, record your interesting sessions, and we will post them for others to share.

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