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The Buddhabrot pattern springs from a simple algorithm: you take thousands of starting points, run each one through the same formula over and over, and chart only those whose values grow without limit—these “divergent” paths form the spectral Buddha-like silhouette. Once you recognize the pattern, you see it everywhere. It’s visible in the rosette stained glass windows of Notre-Dame de Paris and Chartres, numerous representations of the buddha, as well as in the Vāstu-Puruṣa-Maṇḍala used as blueprints for Indian temples, and in the ancient chakra symbols that are now so common—proof that numbers are universal symbols tying Psyche to the world. This is a newly identified archetype: an algorithmic icon born of computation that reveals an underlying cosmic unity that C.G. Jung called the Unus Mundus. Dr. Harry J. Shirley joins us and provides an amazing initiation into this uncanny discovery.
Exploring the Buddhabrot Fractal
Imagine plotting every point in the Mandelbrot equation that eventually flies off to infinity—and then tracing its winding path. That collection of escape trajectories paints the Buddhabrot, a ghostly silhouette that startlingly resembles a seated figure with a pronounced “third eye.” Melinda Green first coaxed this form from simple iterative mathematics, revealing that something as cold and logical as number can yield an image rich with symbolic resonance. You don’t need a PhD in organic chemistry to appreciate how uncanny it feels to see what looks like a cosmic Buddha emerge from pure math. The Buddhabrot isn’t a trick of pixel art—it’s the record of countless numerical journeys. And its haunting beauty begs the question: what deeper connections might link our psyche to this fractal form?
Fractals: Nature’s Blueprint
Fractals are self-similar patterns that repeat at every scale, from the curling tendrils of a fern to the jagged outline of a mountain range. Zoom in on one tiny leaf, and you’ll see the same overall shape as the whole plant; scale that down again, and every twist mirrors its larger counterpart. Benoit Mandelbrot formalized this concept in the 1980s, long after Jung’s death, but its roots lie hidden in nature’s own designs. Fractals optimize growth and energy—think of how a tree’s branches maximize sunlight or how blood vessels spread through your body. Yet despite their complex beauty, fractals arise from deceptively simple equations. That tension—simple rules birthing infinite variety—is what draws a us toward the Buddhabrot’s symbolic resonance.
Unus Mundus: The Underlying Unity
Jung and physicist Wolfgang Pauli coined “Unus Mundus” to describe the primordial ground where psyche and matter merge into One. It’s an echo of Tao, Brahman, or the alchemical “prima materia”—a formless void pregnant with potential. In our everyday ego-driven consciousness, we slice reality into subject and object, inner and outer, but the Unus Mundus resolves that divide providing an archetypal framework suggesting everything springs from a single ordering principle. Harry Shirley’s work proposes the Buddhabrot as visual evidence of this unity—an image where number itself becomes the bridge between mind and cosmos. When you glimpse that fractal form, you catch a shimmer of the Unus Mundus.
Archetypal Geometry in Fractals
Step into any cathedral, Hindu temple, or Buddhist shrine and you’ll find repeating geometric motifs—rose windows, mandalas, and mosaic patterns that resonate with fractal logic. Those sacred designs arose from intuition, centuries before the math was formalized. They gesture toward infinite complexity contained within finite shapes, just like the Buddhabrot. Our ancestors didn’t need MATLAB to see these patterns; they relied on ritual, art, and meditation to tap into an archetypal language of form. Today, we can overlay those ancient images on the Buddhabrot and witness an uncanny match. That visual correspondence sparks awe and critical inquiry: are we projecting meaning, or does number itself carry an archetypal signature?
Chakras and the Third-Eye Connection
Yogic traditions map consciousness along the spine through a series of energy centers or chakras, culminating in the “third eye” at the brow. When Shirley zoomed into the Buddhabrot’s forehead region, he saw shapes echoing the two-petaled third-eye symbol and radiating lines reminiscent of art depicting spiritual illumination. It’s as if the fractal encodes the ascent of consciousness in mathematical form. You can trace a vertical progression of nested bulbs along the Buddhabrot’s midline that parallels chakra imagery from subtle-body art. This isn’t coincidence if you accept that archetypal patterns can surface independently in mind, art, and number.
Numbers as Living Symbols
Jung called numbers “primordial archetypes”—not just abstract tools but living symbols shaping both psyche and matter. Cultures across time and space have rediscovered the same numerical relationships, hinting that number is discovered, not invented. When Newton sat under an apple tree and suddenly grasped gravity, he tapped into these archetypal structures. Likewise, mathematicians like Ramanujan reported dream inspired insights into complex formulas, illustrating number’s link to intuition. The Buddhabrot extends this theme by showing how pure iteration can yield forms resonant with mythic imagery.
From Scientific Artifact to Psyche Mirror
At first glance, the Buddhabrot is a computer-generated curiosity. But when you view it through a Jungian lens, it mirrors inner psychic processes—birth, death, and transcendence of ego boundaries. Those swirling escape paths become a visual metaphor for the unconscious striving to break free from egoic constraints. You feel recognition, as if you’ve glimpsed a dream-symbol plucked directly from the collective unconscious. That subjective resonance doesn’t invalidate scientific rigor; it enriches it by revealing how perception, pattern-seeking, and archetypal memory coalesce.
Individuation Mapped in Mathematics
Individuation—the lifelong journey of becoming one’s true Self—unfolds through stages of confrontation, integration, and transcendence. The Buddhabrot fractal traces a similar ascent from chaotic outliers to coherent form, suggesting a mathematical roadmap for psychic growth. Early iterations produce scattered points, like raw instincts and unintegrated shadow. As you iterate further, a cohesive shape emerges, reflecting the union of Psyche and soma. At its apex, the Buddhabrot’s third-eye motif signals a glimpse of Self beyond duality. This parallel invites us to consider whether fractal patterns can guide inner work, offering a fresh symbolic scaffold for mapping progress.
Collective Emergence and Shared Patterns
Just as no two fern fronds are identical yet all follow the same fractal blueprint, humanity diverges in countless cultures but shares deep symbolic structures. If the Buddhabrot encodes a universal pattern, it implies we are collectively moving toward a new phase of self-realization—what some call collective individuation. By asking “Where are we on the fractal?” we adopt a meta-perspective on societal evolution. Are we stuck in ego-driven loops, or can we collectively experience unity?
Synchronicity’s Mathematical Echo
Synchronicity—Jung’s term for meaningful acausal coincidences—often accompanies moments when inner and outer worlds align. Witnessing the Buddhabrot’s emergence, many report a surge of awe akin to a synchronistic event. You see an image that seems tailor-made for your psyche and instinctively search for parallels in art, religion, and nature. That search itself becomes a participatory dance with the Unus Mundus, where observer and observed collapse. Whether you label this pattern-matching as cognitive bias or archetypal revelation, the experience demands you weigh reason against mystery.
Sacred Geometry Reimagined
Sacred geometry—circles, triangles, spirals—has guided architects and mystics for millennia, yet it remains an approximation of deeper fractal laws. The golden ratio in a Parthenon façade or sunflower seed head hints at similar scaling but falls short of infinite iteration. The Buddhabrot offers a more precise template, showing how simple formulas generate endless complexity. When you overlay sacred motifs on fractal renderings, the fit can be uncanny. This suggests that our ancestors intuited fractal principles through art and ritual, long before computers existed.
The Ego’s Hesitation and Compensation
The ego recoils when asked to relinquish its sense of control—to see itself as part of a larger, numinous order. Yet Jung posits Psyche compensates for one-sided attitudes, and the Buddhabrot embodies that compensation for rationalism. It confronts modern Western sensibilities with a form that is both mathematical and mystical, demanding we hold a paradox. You can’t reduce it to data visualization without losing its symbolic charge; nor can you dismiss it as mere fantasy without ignoring its empirical roots. That push-pull provokes an inner dialectic: can you tolerate the mystery implicit in measured form?
Bridging Rationality and Mystery
We’ve been trained to regard math and myth as strangers—one coldly logical, the other wildly intuitive. The Buddhabrot invites you to sit at their intersection and listen. It shows that rigorous iteration and poetic meaning need not live in separate cylinders. You might approach it as a data scientist tracing escape or as a seeker gazing at mandala-like patterns; both views yield insight. Holding them together disrupts the false dichotomy between head and heart, calculation and contemplation. In practice, this means cultivating “both/and” thinking instead of “either/or” choices. That shift alone can redefine how you approach puzzles in therapy, art, or daily life.
Holding Tension for Transformation
At its heart, the Buddhabrot teaches you to hold dualities without collapsing into one pole or the other. You learn to tolerate the rational marvel of simple equations birthing infinite complexity, while staying open to the mystical invitation they carry. That tension is the crucible of transformation: only by dwelling in the in-between can new insights crystallize. You don’t need to resolve every paradox; you need to linger in the creative discomfort it provokes. Each time you revisit the fractal, you may catch a fresh shimmer of meaning, a new resonance with your own process.
Dr. Harry J. Shirley
Dr. Harry J. Shirley holds a PhD in Organic Chemistry from the University of Oxford and spent several years in academic research before transitioning into scientific consulting. After encountering Jungian psychology through his own psychotherapy, he became fascinated by alchemical symbolism and the question of how mind and matter interrelate. By chance, he discovered that plotting the escape trajectories of the Mandelbrot equation yields the “Buddhabrot” fractal—a form whose glowing third‐eye silhouette and self-similar lobes echo patterns in sacred art and spiritual diagrams. In his peer-reviewed article The Buddhabrot and the Unus Mundus, Shirley conducts a qualitative comparative analysis showing how this fractal may constitute a newly revealed archetype, a mathematical icon that bridges empirical science and the collective unconscious.
Learn more about the Buddhabrot HERE
Read his paper, The Buddhabrot and the Unus Mundus.
You Can Support Dr. Shirley’s Work HERE
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Deb you wondered about how developmental psychology could be effected by the Buddhabrot and its associations with Unus Mundus. What immediately came to mind was Erik Erikson’s eight developmental stages, but more importantly Joan Erikson’s (Erik’s wife) work on the ninth stage gerotranscendence. Joan based her ninth stage of human development on Lars Tornstam’s work on gerotranscendence which is fascinating and includes “an increasing feeling of cosmic communion with the spirit of the universe; a redefinition of the perception of time, space, and objects; a redefinition of the perception of life and death and a decrease in the fear of death, an increased feeling of affinity with past and coming generations, a decrease in interest in superfluous social interaction, a decrease in interest in material things, a decrease in self-centeredness and an increase in time
spent in meditation” (Tornstam, 2005, p. 41).
I know the above because it was part of my dissertation where I followed around nine highly transcendent, generative, and wise older adults – LOL. So just had to pitch this in.
Great job on the connection with Harry!