To Figure:

To form or shape, to trace, to reckon or calculate, to represent in a diagram or picture, to ornament or adorn with a design or pattern.

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The Institute does not yet have a physical space, but our permanent location in the conceptual landscape is on the edge of this iconic fractal.
The IFF as located on the Mandelbrot Set.

The Mandelbrot Set belongs to a class of mathematical objects knows as fractals, whose dimension is always a fractional quantity.
See more about fractals.

Though infinitely complex in form, many fractals are surprisingly easy to generate
Generating fractals.

Instructions for making the Koch Snowflake
Diagram courtesy Larry Riddle, Department of mathematics, Agnes Scott College.

Begin with an equilateral triangle.

Scale it by a factor of 1/3 and place from IFF BROCHURE
copies of the smaller triangles along each side of the original. Scale again by 1/3, and once more place copies of the smaller triangles along all sides of the larger figure. Repeat ad infinitum. The edge of the Koch Snowflake – the so called Koch Curve - and was the first fractal form discovered.

 

Image of a Koch Curve

“It is this similarity between the whole and its parts, even infinitesimal ones, that makes us consider this curve of von Koch as a line truly marvelous among all. If it were gifted with life, it would not be possible to destroy it without annihilating it whole - for it would be continually reborn from the depths of its triangles, just as life in the universe is.”

- Ernesto Cesaro (1905)

Atti della R. Accad. Sc. Fis. Math. NapoliThough finite in geometric extent, the Koch curve is infinite in length. Like other fractal curves it is poised between a line and a plane, a topological ambiguity that enables its depthless internal complexity. Where a line has one dimension and a plane has two, the Koch curve has a “fractional” dimension of 1.26. Coastlines, clouds and other fractal structures all possess a fractional dimension. The dimension of the west coast of Britain has been measured at 1.25.

Sierpinski Carpet: Discovered in 1916 by the Polish mathematician Waclaw Sierpinski, this fractal is generated by cutting a hole in the middle of a square, and repeating this step indefinitely. The carpet has a dimension of 1.8928
Fractal structures may be linear (one dimensional), planar (two dimensional), volumetric (three dimensional) – or any higher dimensionality. One of the most famous fractals is the Menger Sponge, the three-dimensional analog of Sierpinski’s carpet. The dimension of the sponge is 2.7268.
 
© 2005 The Institute for Figuring