Particle-Wave Conversion.In a similar fashion, astrology has always viewed particles as wave forms and vice versa. For example, the cycle of a planet, viewed over spacetime, is really a wave form (where these wave forms intersect, we have points of contact called aspects). Whether light or a unit of energy called the electron was really a particle or a wave was one of the first questions that quantum physics had to address, and it discovered that they really are both, behaving different ways in different situations. It was a shock to scientists to see a photon behave as a particle in one experiment and as a wave in another (for example, a single thing manifesting in 'two places at once'). But Astrology has always recognized this, treating planets at different times as particles (for example, in the natal chart) and as wave forms (in transit or progression). But they are the same planet.

The Mandlebrot set is a mathematical equation composed of real and imaginary numbers developed by the Polish mathmetician bearing its name. The set originated as the bug-like image at the center. Zooming in on any portion of the image will produce a repetition of the original set. What appears to be chaos is really a highly ordered matthematical pattern, much like the rest of reality.

Benoît B. Mandelbrot is best known as the "father of fractal geometry." Although Mandelbrot invented the word fractal, some objects featured in The Fractal Geometry of Nature had been previously described by other mathematicians. However, they had been regarded as isolated curiosities with unnatural and non-intuitive properties. Mandelbrot brought these objects together for the first time and turned them around into essential tools for the long-stalled effort of extending the scope of science to non-smooth parts of the real world. He highlighted their common properties, such as self-similarity (linear, non-linear, or statistical), scale invariance and (usually) non-integer Hausdorff dimension.

He also emphasized the use of fractals as realistic and useful models of many phenomena in the real world that can be viewed as rough. Natural fractals include the shapes of mountains, coastlines and river basins; the structure of plants, blood vessels and lungs; the clustering of galaxies; Brownian motion. Man-made fractals include stock market prices but also music, painting and architecture. Far from being unnatural, Mandelbrot held the view that fractals were, in many ways, more intuitive and natural than the artificially smooth objects of traditional Euclidean geometry.

The boundary of the Mandelbrot set is a famous example of a fractal.