Fractal metaphysics is a general term encompassing all adaptations of fractal geometry to areas that are primarily non-physical and non-mathematical. Usages of this sort are controversial, particularly among mathematicians.

There are three major types of fractal metaphysics:

Fractal Mysticism

Fractal mysticism is the loosest and least rigorous of the three types. In it, fractal artworks are used as a framework for spiritual journeys, much in the same way as are mandalas. The ideas, terms and concepts of chaos theory are used as inspiration, but little effort is made to create solid correlations.

Recursive shapes such as fractals have been a favorite of mystics for quite a long time, as (for example) the "wheel within a wheel" of the Biblical prophet Ezekial or the successive decompositions of yin and yang in Taoism.

Fractal Metaphor

The term "irrational" can be applied to a person or an action, but comes from the ancient geometric concept of ratio. In the same way, the new geometry of chaos has given new terms and concepts (such as "strange attractor") that can be applied profitably outside of their field of origin.

Fractal Philosophy

Finally, there is a small but growing group of thinkers who are trying to apply fractal geometry and chaos mathematics directly and rigorously to non-physical ideas such as virtue, motivation, community, purpose, social structure and so forth.

In Plato's classic work The Republic, the noble city is described as having the same tripartite structure as the soul of a single noble inhabitant of that same city. This can be described geometrically as a large shape made of small copies of itself --a description that also holds true for many fractals such as the Sierpinski gasket.

The same process can also take place in reverse, however. If we start with a shape such as a Sierpinski gasket (a triangle divided into smaller triangles, each of which is divided into yet smaller triangles, and so forth) it is possible to design a hypotheical social structure which duplicates the same set of relationships. For instance, we could picture a nation, made of three states, where each state comprised three regions, and each region consisted of three communities and so forth, down to a basic level consisting of small groups made up of three people each.

An attempt to connect the social properties of a political network patterned in that manner to the mathematical properties of the Sierpinsky gasket that underlies it would be a fractal philosophy.

See Also

• fractal
• chaos theory
• metaphysics
• mysticism

External Links

• Fractal Metaphysics Home Page
• Trifractal Analysis: An application of fractal geometry to social structure.