Fractals and spirals emerge all around us – fascinating mathematical and natural forms that seem to connect the dimensions of the physical world, symbolic imagination, and the human psyche. From the whorls of a rotating galaxy to the veins of a fern leaf, through psychedelic designs and mystical mandalas, these recurring patterns suggest that there are fundamental structures underlying reality.
Humankind has constantly explored the meaning of these patterns.
How do chaotic equations produce ordered forms? Why is the spiral a universal symbol of growth and continuity? And what can these forms reveal to us about the collective unconscious and processes of personal or collective transformation?
Exploring these motifs invites us to uncover the deep connections between these questions.
Fractals and Spirals in Nature: Universal Patterns
A striking feature of nature is the omnipresence of self-similar patterns, repeating the same structure at different scales. Fractal geometry was specifically developed to describe these “infinitely fragmented” forms.
Mathematician Benoît Mandelbrot, a pioneer in the field, noted that “clouds are not spherical, mountains are not cones, coastlines are not circular, and tree bark is not smooth, just as lightning does not trace a straight line.”
In other words, the forms of reality do not conform to simple geometries (spheres, cones, straight lines). They follow a more complex order.
By introducing multiple equations to model seemingly chaotic phenomena, Mandelbrot was surprised to find that the result did not illustrate the expected “chaos.” Instead, the curves were orderly and regular at all scales.
Mandelbrot’s fractal produces, at each level of zoom, new arabesques and spirals similar to the global shape, revealing an infinite depth in a simple equation. It thus illustrates how a process can generate seemingly limitless complexity – an image of infinity nested within the finite.
Living nature provides many examples of fractals, where each part reproduces the appearance of the whole. Cabbage, fern, rivers, trees, to name just a few.
Scientists have found that a fractal organization governs the structures of the human body (bronchi, blood network, neural systems, etc.), as well as many geological and cosmic phenomena.
The same pattern of form seems to manifest from clouds to coastlines, forests to lightning, and even in the distribution of galaxies in the Universe.
Fractals capture something essential about the organization of reality: nature weaves its patterns with “long threads,” so that each small piece of its fabric reveals the organization of the entire tapestry.
In other words, every fragment of the world, no matter how modest, can reflect at its scale the order of the whole.
Spirals form a particular and captivating case of these universal patterns. They are found at all scales of living and physical worlds.
The shell of a snail, the horns of a ram, a flower petal, a pine cone, seashells... Nature seems to favor the spiral. The mathematical laws explaining these plant spirals suggest that there is a principle of geometric harmony in organic growth.
Even in the inanimate scale, spirals appear in atmospheric cyclones (satellite view of a hurricane) or in the majestic structure of spiral galaxies.
These cosmic spirals remind us that the same patterns are found at the astronomical scale, possibly expressing a fundamental architecture of nature.
These correspondences inspired the idea of a fractal universe, where each part would contain the information of the whole – a concept that strongly resonates with ancient philosophical intuitions.
Spiritual Symbols: Spirals of Life and Visions of Infinity
Beyond their tangible existence, fractals and spirals have always fascinated human imagination and held a prominent place in symbols. The spiral, in particular, is one of humanity’s oldest symbols.
It is found engraved on prehistoric artifacts in Europe, often associated with feminine figures of fertility or natural cycles.
Around the world, the spiral is linked to ideas of life, movement, and renewal.
In many African cultures, it is associated with the cyclical movement of life and represented by the serpent that bites its own tail and coils around itself – an image of fertility and the eternal cycle. This serpent is related to the Ouroboros, a universal symbol found from ancient Egypt to Norse mythology, depicting a serpent biting its own tail to form a perfect circle. The Ouroboros expresses eternal return, the unity of opposites, and the cyclical nature of existence, where the end and the beginning merge into one.
The spiral, for its part, differs from the circle in that it progresses outward or inward: it is a circle that opens, that evolves.
Thus, many traditions have seen it as a symbol of development and expansion.
The Hermetic principle formulated by Hermes Trismegistus, “As above, so below,” evokes this correspondence between the microcosm and the macrocosm.
One could say that the individual contains, fractally, the same cosmic plan that structures the entire universe.
This idea, found in esotericism and alchemy, affirms the fundamental unity of the world.
Each individual soul reflects the Whole, just as each fractal pattern repeats the form of the grand whole to which it belongs.
In Eastern spiritual traditions, similar images can be found. Mahayana Buddhism uses the metaphor of Indra’s net to describe universal interdependence: the universe is pictured as a vast network of jewels, where each jewel reflects all the others infinitely.
Other examples abound. Tibetan mandalas can be seen as an attempt to represent infinity and totality through a geometric diagram. The very term “mandala” (sacred circle) intrigued Carl Jung, who saw it as an archetypal image of the Self (the psychic totality).
One could also cite Sufi poets, who sang of the structure of the atom, the rotation of electrons around the nucleus, the dance of clouds, and cosmic cycles, poetically expressing the hidden order in chaos long before the formalization of fractals.
Science, art, and mysticism seem to converge here, driven by the same aspiration: to decipher the secret order of the world and our intimate connection with it.
The fractal, by definition, suggests a pattern that repeats endlessly at a smaller scale – one can see it as a visual analogy of infinity and eternity. The spiral, in turn, with neither clear beginning nor end as it unfolds, evokes this boundless continuum.
Contemporary visionary art often draws heavily on fractal and spiral imagery (think of the psychedelic works of Alex Grey) to illustrate the idea of a multidimensional, infinitely deep reality in which the soul can travel.
These geometric patterns, often experienced under intense meditation or entheogenic substances, are interpreted by some as the “signature” of an underlying cosmic order. A kind of universal language of creation revealed to expanded consciousness.
Whether one subscribes to these visions or not, the evocative power of the spiral and fractal remains: both point to the idea of an infinity present in everything, a mystery in abeyance where each level reflects a higher one.
Collective Unconscious and Transformation: The Echo of Archetypal Patterns
Carl Jung, the founder of analytical psychology, was deeply interested in the universal forms taken by human imagination. He called these archetypes of the collective unconscious.
According to Jung, beyond our individual experiences exists a “universal psychic reservoir” filled with patterns and symbols common to all humanity.
These archetypes (the Wise Old Man, the Mother, the Hero, the Shadow, the Self represented by the mandala, etc.) manifest in myths, dreams, religions, and reflect deep psychological dynamics.
Many of these archetypal symbols are geometric or natural in nature: the mandala, the cross, the tree of life, the serpent…
Jung noted that spontaneously, his patients in therapy would draw mandalas or concentric patterns when a process of personality re-centering was underway. To him, these forms were not mere drawings, but the visible expression of an inner reorganization toward greater wholeness and balance.
The spiral is part of the images of psychic progression that Jung discussed.
He saw it as representing the process of individuation, the journey by which an individual transforms and realizes their Self.
The spiral illustrates that as we move along our path, we revisit places already visited, but at a higher level. In other words, personal evolution is not a straight line, but an ascending spiral: we revisit old issues, but with more awareness at each cycle.
This idea resonates with philosophical concepts of eternal return (Nietzsche) or history that stutters (Hegel), where the new is born from the repetition of the cycle at a different level.
The symbol of the Ouroboros perfectly illustrates this principle of cyclical transformation. Jung wrote extensively about this archetype of the serpent biting its tail.
The Ouroboros represents the idea that the end meets the beginning, that death prepares for rebirth. It is a symbol of integration of the self and inner evolution. The image of the Ouroboros expresses the union of opposites. It is both devouring and devoured, life and death.
In our lives, we experience this cycle during major transitions: a part of us must die (old habits, outdated beliefs) so that another may be reborn renewed.
The spiral movement, like the Ouroboros, inscribes this drama of transformation within a sacred temporal unfolding: what returns is never exactly the same, there is hidden progress in the repetition.
Interestingly, researchers have drawn parallels between fractal structures and the functioning of the collective psyche. The human mind spontaneously produces patterns that can be called fractals or chaotic, such as in associations of ideas or brain rhythms.
Some psychologists see in Jung’s archetypes a kind of “psychic fractal”: fundamental patterns that repeat across cultures and ages, forming recognizable figures in the mythologies of the world.
Just as a simple equation generates a complex fractal, a few fundamental themes of the soul would give rise to an infinity of variations of myths and symbols.
Jung himself, a great lover of mathematics, was interested in the properties of numbers and geometric figures as archetypes of cosmic order.
In his exchanges with physicist Wolfgang Pauli, he explored the hypothesis that the structures of the psyche and those of matter might have a common origin in a deep level of reality.
Pauli and Jung discussed the phenomenon of synchronicity, these meaningful coincidences without causal link. They foresaw a unifying principle connecting the mental and physical, beyond apparent duality.
This idea resonates with the notion proposed by physicist David Bohm of an implicit order: a hidden order in which all information of the universe is holistic and connected, the explicit order (our phenomenal reality) being merely the visible unfolding of this underlying framework.
One could imagine that Jung’s collective unconscious is part of this implicit order. A kind of reservoir where all human experiences are connected, just as fractal structures suggest a common weaving linking each local detail to the global form.
Thus, fractals, spirals, and archetypes share a logic of repetition at different scales.
The human psyche has always used motifs such as mandalas, labyrinths, or cosmic trees to represent its relationship with the world, as if it intuitively knew that each soul is a reflection of the entire universe.
Similarly, our paths of personal transformation often follow a spiraling path, made of crises and successive renewals, like the natural cycles of seasons or the shedding of the serpent.
Societies too evolve in spirals: history seems cyclical, but each era brings a new level of complexity.
Behind the chaos of the world slumbers a unified order – a primordial pattern in perpetual transformation.
Hidden Order, Unity, and Metamorphosis: Crossed Perspectives
Our exploration reveals a central theme: that of the hidden unity behind changing forms.
Spirals and fractals teach us that the multiple can arise from the repetition of the One.
Fractal geometry and chaos theory have shown how forms of astonishing beauty can emerge from simple mathematical laws. The apparent disorder of the world hides a subtle design more ordered than it appears.
Philosophers and sages of many traditions have often affirmed that a single Principle (which some call Tao, Brahman, God, Grand Architect, etc.) underlies the infinite variety of beings.
Fractals offer a powerful visual metaphor for this metaphysical intuition: like a fractal pattern, the Absolute would manifest at all scales of creation, each creature carrying within it the spark of the Whole.
This is the Hermetic idea
“As above, so below,”
or the Hindu notion that the atman (individual soul) is identical in essence to Brahman (universal soul).
In modern language, we would speak of the “source code” of the Universe: each fragment would contain the information of the whole, fractally and holographically.
On a philosophical level, these patterns also invite us to reflect on time and change. The spiral combines the idea of return and linear progression. It is both cyclical time and linear time.
Thinkers like Mircea Eliade distinguished between sacred time (cyclical, ritual, returning to itself) and historical time (linear, oriented toward a goal).
The spiral could serve as an emblem for a vision of time that reconciles these two aspects: history repeats itself, but each repetition takes place at a new turn of the spiral, bringing something new.
There is a consoling depth here: nothing ever completely disappears, everything transforms. Death nourishes life, ends announce new beginnings in a great cosmic recycling.
Heraclitus said “everything flows” (panta rhei), but we could add: everything turns and returns in a new form.
Understanding that we are part of a larger pattern can encourage humility and respect. If we admit that the universe is a fabric of which we are but a thread (as physicist Feynman suggests), then our individual actions resonate beyond ourselves.
Everything is connected.
Seeing our life journey as an evolving spiral allows us to approach crises as necessary phases of metamorphosis, where the old “self” dissolves so that a new one may be born, more complete.
This is the symbolism of the butterfly emerging from its chrysalis or the phoenix rising from its ashes, images that are themselves very fractal.
Conclusion.
Fractals and spirals offer a common language for modern science, philosophy, and spirituality to think about the architecture of reality.
They show us a universe where the simple and the complex, the one and the many, order and chaos are intimately intertwined.
In this universe, each small fern leaf can tell, in its own way, the same story as the entire forest; each human being, through their dreams and myths, replays themes that have resonated at the heart of humanity since the dawn of time.
This awareness, cherished by Jung, the sages of India, and quantum physicists, opens the door to profound personal and collective transformation. Because if we are aware that we are part of a great pattern that surpasses us, we can align our lives with this harmonious order, following the current of the spiral rather than resisting it.
Our inner transformation is part of a vast evolutionary process – an infinite dance where the particular and the universal continually marry, like a fractal pattern in perpetual expansion.
© NOIR KĀLA
Sources :
Benoît Mandelbrot, La Géométrie fractale de la nature, 1977
Carl Jung, L’homme et ses symboles, 1964
David Bohm, Wholeness and the Implicate Order, 1980
Fritjof Capra, Le Tao de la physique, 1975 ; La Toile de la vie, 1996
L’Avatamsaka (Hua-Yen), écrit ancien, principalement compilé entre le 4e et le 7e siècle, dans ses différentes traductions et versions modernes
Photography : Bianca Des Jardins
