Fractal Mathematics and Jungian Archetypes with Harry Shirley

Oct 13, 2025

Harry Shirley, a chemist turned Jungian psychology enthusiast and author, delves into the intriguing intersection of fractal mathematics and archetypal symbols. He explains how fractals like the Mandelbrot set reveal deep symbolic insights into our psyche, connecting mathematics, alchemy, and spirituality. Shirley relates the Buddhabrot to archetypal mandalas, explores the Unus Mundus as a unified realm of mind and matter, and discusses the symbolic significance of numbers in our understanding of the self and reality.

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INSIGHT

Fractals As Nature's Geometry

Fractals are not merely abstract math but the way nature creates geometry and order.
Harry Shirley sees spirals, coastlines and plant shapes as evidence of ubiquitous fractal dynamics.

INSIGHT

Mandelbrot's Symbolic Richness

The Mandelbrot set is a simple complex iterative formula that generates infinite, self-similar mandala-like borders.
Shirley notes the set contains familiar constants (pi, e, Fibonacci) and echoes patterns reported in psychedelic visioning.

INSIGHT

Buddhabrot As Visualization Shift

The Buddhabrot is not a different equation but an alternative visualization of the Mandelbrot that traces escaping paths.
Melinda Green's visualization revealed images evocative of Eastern deity forms like Buddha and Ganesh.

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Fractal Mathematics and Jungian Archetypes with Harry Shirley

Dr. Harry Shirley is a chemist with a deep interest in Jungian psychology. His paper The Buddhabrot and the Unus Mundus: A Qualitative Exploration of Fractal Patterns and Archetypal Symbols was recently published in the International Journal of Jungian Studies. He is based in the United Kingdom.

In this interview, Dr. Shirley explores the fascinating relationship between fractal mathematics and Jungian archetypes. He discusses how fractal imagery such as the Mandelbrot and Buddhabrot reveal symbolic dimensions of the psyche, connecting mathematics, alchemy, and spiritual traditions across cultures. This conversation opens new perspectives on the Unus Mundus, the Self, and the archetypal foundations of number and pattern.

New Thinking Allowed host, Jeffrey Mishlove, PhD, is author of The Roots of Consciousness, Psi Development Systems, and The PK Man. Between 1986 and 2002 he hosted and co-produced the original Thinking Allowed public television series. He is the recipient of the only doctoral diploma in “parapsychology” ever awarded by an accredited university (University of California, Berkeley, 1980). He is also the Grand Prize winner of the 2021 Bigelow Institute essay competition regarding the best evidence for survival of human consciousness after permanent bodily death. He currently serves as Co-Director of Parapsychology Education at the California Institute for Human Science.

(Recorded on September 11, 2025)

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