Sunday, May 7, 2023

Giaome Biogenesis

"Gaiome Biogenesis"
(Pencil & compass drawing)
* * * 
"As with one eye there is no perception of depth, so with one biosphere our view of the universe lacks depth.  A multiplicity of biospheres not only creates specific new angles of vision; it multiplies perspectives. It may also produce a whole new kind of vision, a sort of biological "hyperspective."" - Dorion Sagan

This is about trying to create a symbol for the idea of biospheric bifurcation, the multiplying of our earth's biosphere and our perspectives on life, evolution, and the earth, ensuring an evolutionary multi-planetary future for our species in the solar system. Evolving both humanity and the biosphere together by exploring the idea of engineering outer earth orbiting biospheres, self-sustaining planetary ecologies, and the idea of “eco-technics”; where permaculture meets astrophysics, and where natural intelligence meets artificial/sentient intelligence. 

The leaves and eyes represent the unfolding of this potential cosmic biogenesis inherent in natures intelligence, and the Apollonian fractal circle gasket represents the multiplying of earth into biospheres.

Overall, we can see the self-organizing, self-sustaining, and self-regulating dynamics of nature and the biosphere as a decentralized but holistic “technology”—an organic self-designing self-intelligent evolutionary systems technology running throughout all of life, that we can interact with in evolutionary ways that open emergent adaptations, transformations, and outcomes.
"We cannot conquer nature with our technology, but we can conquer our technological nature: by working with nature, by conceiving of life as a whole integrated organism of which we are part, we can use our ingenuity for the benefit of all life - and be the more human for it." - Dorion Sagan 


"Earth Mitosis"
(Pencil & compass drawing)


"Reproducing biospheres represent a new hour in the human day, a new age in the Earth's ontogeny. If we could examine history under the temporal equivalent of a microscope, we might be startled by the resemblance to organisms and cells of biospheres." - Dorion Sagan 
"We need a new story. We need a story that actually comes out of what we know about the universe. That's our moment." - Brian Swimme

"The ultimate importance of the evolutionary vision lies not just in its power of unifying scientific thinking and stimulating a truly transdisciplinary approach, but also in the philosophy it expresses--a philosophy close to life and its creativity. The alienation of science from life, which has become a matter of growing concern, is about to be overcome by the evolution of science itself." - Erich Jantsch

“I live on Earth at present, and I don’t know what I am. I know that I am not a category. I am not a thing — a noun. I seem to be a verb, an evolutionary process – an integral function of the universe.” - R. Buckminster Fuller

“Successfully running a new biosphere would show people what it takes to make it in our beloved old one.” - Dorion Sagan & Lynne Margulis 


Gaiome: Notes on Ecology, Space Travel and Becoming Cosmic Species

Biospheres: Metamorphosis of Planet Earth

Dr. Bruce Damer:  S.H.E.P.H.E.R.D. Asteroid Capture and Handling


Friday, April 21, 2023

Phi-Eye and the Golden Circles

Pencil and compass drawing, digitally altered
* * *
“I see through my eyes, not with them.”
— William Blake


The Golden Cut (1:1.618...) creating the Golden Circles 
overlapping within the vesica piscis
* * *
“You will know, as far as it is allowed to a mortal, that nature is from all points of view similar to itself.” — Pythagorus

George Leoniak’s discovery of the Golden Circles template and the many different geometric connections that it makes possible really starts to open the doors of the phi ratio relationships in a very consistent way in your connection with geometry—no matter what level you’re at. 

The template, consisting of series of phi ratio proportioned concentric circles, in either 2, 3, or 5-fold view, makes working with sacred geometry altogether a more easily expansive and insightful practice, not only in the capacity to discover and construct forms, but in its ability to integrate the interconnected meanings of the root relationships, ratios, and perspectives more simply and coherently.

The Golden Circles are like a meta-organizing pattern to see the whole field of sacred geometry anew through. Exploring them is like interacting with a type of psychoactive auto-didactical generative tool for catalyzing new geometric connections and epiphanies; it is a way of keeping geometry in check with both the absolute transcendent, its source, and also the dynamic of life and phi as it emerges and connects back to source; both with the One and all its emergent self-similarities.


Three Golden Circle views:

2-fold/square view

3-fold/hexagon view

5-fold/pentagon view

Overall I find this approach a more holistic way of exploring and understanding what sacred geometry is, you could say it literally puts the proportional dynamic, the life of phi into the Flower of Life, or what Keith Critchlow more appropriately termed the “Flower of Creation.”

The basic version of the Golden Circles Seed of Life pattern is a simple and elegant complement to the traditional Flower of Life pattern. The Golden Circle lattice is in phi proportion and fits in between the familiar central 6-fold petals of the Seed of Life and Flower of Life patterns, giving an interaction and overlap between √3 and √5 geometries, showing us a richer field of interconnected circles for new connections, coordinates, and potentials for forms to emerge.  

The Seed of Life & Golden Circles, 
(blue circles are phi ratio/ √5, red are √3 )

Golden Circles Flower of Life

Working with the Golden Circles method incorporates multiple views and construction methods, both in what it does for understanding and discovering accuracy in the various solids and polyhedra based on phi, and in how it uses both digital and traditional compass methods for exploring and checking accuracy and creation method, and also 3-D construction.

A good example of this is how the Golden Circles method corrects the popular Metatron's Cube method of constructing a true dodecahedron. The difference is subtle but once you see it you can't unsee it. The dodecahedron created from the hexagon view of the Metatron's Cube method is not just a perspective or perceptual issue, it's a fundamental problem because it's not made from even-sided pentagons, and definitely not proportional to phi ratios, and so it cannot be constructed into an actual 3-dimensional form. 

(Images from George Leoniak)

Metatron method compared with Golden Circles Method

Golden Circles method - Nested Dodecahedrons
* * *

Engaging with this phi based method or key to further opening the secrets of the circles of the Flower of Life allows the sacred and symbolic aspects and the of the unity of geometry, or harmony of the constants, to emerge as internal insights into the eternal that happen when you do the work and make the connections and interact with the mystery and your own curiosity and creativity.


Below are some of the various polyhedra studies, created from using the Golden Circles template pattern and variations, discovered & taught by George Leoniak and Knew geometers at Knew Geometry — (check out more on his work, courses, and group here: — Knew Geometry Youtube — Knew Geometers FB Group)

"The world around us is a world of numbers—numbers that spell life and harmony. They are organized by the geometry of figures, all related to one another according to a sublime order, into dynamic symmetry.
Glimpses into this magnificent kingdom form the basis of all our knowledge and it seems that in this domain the ancient civilizations had gone further than modern science." 
— Paul Jacques Grillo, Architect (1960) 


Golden Circle Polyhedra Studies

Dodecahedron from Golden Circles with √2 radius circles

Truncated Dodecahedron from Golden Circles with 0.618 outer circles 

Icosidodecahedron from Golden Circles

Truncated cube from Golden Circles with √2 circles

Great Rhombicuboctahedron from Golden Circles with √2 circles

Rhombicuboctahedron from Golden Circles with √2 circles x2

Rhombicosidodecahedron from Golden Circles 

Truncated Icosahedron "Buckminsterfullerine" from expanding Golden Circles 

Rhombic Enneacontahedron inside Dodecahedron from expanding Golden Circles

Great Rhombicosidodecahedron from Flower of Life with Golden Circles x4

Great Stellated Dodecahedron Star Polyhedron from Golden Circles

Small Stellated Dodecahedron from Golden Circles

Icosahedron front view from Golden Circles


Saturday, December 17, 2022

Self-Organizing Bio-Logic

"Self-Organizing Bio-logic"
Digitally altered drawing, 2017

The poet Goethe was actually one of the first pioneers of the sciences of complexity and emergence. He found a dynamic participatory way of seeing nature, documented in his study on the metamorphosis of plants. He was one of the first to explore what a non-reductionist and vision-logic imaginative level of archetypal thinking can be, seeing a unitive evolutionary archetypal process at work in nature, and in perceiving and thinking about nature, or in other words a gestalt way of seeing the whole.

Applying Goethean Science or a gestalt mode of inquiry is essential to better grasping the order of process and dynamic complexity of the natural world ..

"If the scientist is too bigoted to feel himself into the sensibility and the living values of the artist, he will propose only dead structures." - Jacob Bronowski

“The holistic paradigm, Gaia, deep ecology, and new alchemy all have a hidden ancestor: Johann Wolfgang von Goethe.” - John Barnes


“In Goethe's method, "how" to look is the key. We must switch our attention away from the verbal-intellectual mind and into "seeing." This way of seeing is active, not passive. We plunge into seeing the qualities of the phenomenon. This takes us away from the uniformity imposed on nature by the intellectual mind and we experience the non-uniformity, richness and diversity of the world. 

In this way we arrive at the simplest case, the "pure phenomenon," the part that contains the authentic whole. This is the aim of the first stage of Goethe's method. What is particular in our normal way of seeing becomes universal in the intuitive mode. Goethe described the pure phenomenon as " an instance worth a thousand, bearing all within itself." The classic example is found in Goethe's observation that "all is leaf." For the rational mind, the leaf is just one part of the plant along with the petals and stamens. These parts are regarded as essentially separate and independent of each other. But with the switch to the intuitive mode of consciousness the leaf is understood in a universal sense as an "omnipotential form," rather than as a particular physical leaf.

The process of active seeing is deepened in Goethe's subsequent stages, in "exact sensorial imagination," or guided imagery. We visualize the phenomenon in imagination. This is sensory and concrete, not abstract, attention is withdrawn further from the verbal, and consciousness is restructured into an "organ of holistic perception." The purpose of this stage is to realize an element of the phenomenon not given to sense experience. 

This is the law, the organization or unity of the phenomenon. The intuitive understanding of the leaf, the one single organ, allows us to grasp the continuity of form of the plant. We can visualize the "coming into being " of the plant, its metamorphic sequence. 

With a reversal of perception, the universal is not a generalization abstracted from the particular; it is perceived as "shining in the particular." We see not an assemblage of parts, an analytical snapshot; we see the intensive depth of the plant, another dimension in which "it shows itself as itself.”” 


“Who would study and describe the living starts

By driving the spirit out of its parts:

In the palm of his hand he holds all the sections,

Lacks nothing, except the spirit’s connections.”

- Goethe, Faust


"Leaf Field"
Digitally altered drawing, 2015

Saturday, October 29, 2022



Oil on canvas, 70” x 40”



The word "metacosm," is defined as a system that encompasses cosmos systems, both the macrocosm and microcosm, as a transcendent field of forces that is beyond the created world. I didn't know this word at the time of first thinking about this painting and idea but it really fits with what I am trying to show with this piece. Especially how it relates to the torus geometry, and how it is a type of meta-archetype or pattern in sacred geometry, that shows up in the way the universe organizes itself at all scales, from atoms to cells to planets to stars to galaxies. 

Metacosm is about imagining the cosmos as an infinite fractally nested self-generating and self-creating bifurcating multiverse, which if bifurcating inside of itself infinitely at every plank length instance of difference/expansion, could represent a branching parallel torus universe structure (or metaverse) within the metacosm, that would be a way of thinking about a 5th dimensional view of 4th dimensional emergent bifurcating timelines or universes, or a 2-D slice of 4-D branchings within a 5-D concept.

"This is a creating universe not a created one." 
— Walter Russell



The drawings for this initially where rough sketches of torus forms trying to find a shape and order that could nest within itself, which then lead to being laid out within an inverse square grid, with the torus as an expanding field/universe within a circle shape.

Initial drawings for Metacosm

It wasn't until recently when I discovered George Leoniak's geometric construction for the mathematics of the golden ratio that I realized how the Metacosm torus geometry and nested torus pattern can formatively interrelate with the phi ratio circles, the vesica piscis circles, and the circles from the inverse harmonic square grid pattern. 

George Leoniak's geometrical construction from the mathematical equation of the golden 
ratio (√5+1 divided by 2 = Phi (1.618…)) created from the vesica piscis. 

Circle geometry for the golden ratio equation overlaid onto Metacosm

Metacosm geometry studies - Phi ratio circles/Torus/Square grid.


The torus archetype, which is closely connected to the circle and vesica piscis, is both an archetypal field-form that is transcendent, beyond all creation, like the circle, and connected to the notion of the whole as a sphere, but then also is an archetype very present in natures way of organizing energy and matter into flows, vortexes, and cycles, into self-reinforcing self-organizing patterns or fractals, in matter and life and mind. 

As an archetype it seems specially preordinate, a-priori, and nondual, because it is both a formative transcendent background and static unchanging constant, but also an archetype of dynamic self-organizing fields, and emergent complex systems. It is an archetype transcendent of form but while also being emergent with dynamic form; both an archetypal blueprint-form, and an archetypal formation pattern of self-organizing fields. 

In short the torus is both a transcendent meta-structure and emergent meta-pattern, both macrocosm and microcosm; both above, and below; a Metacosm.

"The indication is of the notion of a plane of being that's behind the visible plane, and which is somehow supportive of the visible one to which we have to relate. I would say that's the basic theme of all mythology, that there is an invisible plane supporting the visible one."  Joseph Campbell

"Spiritual science seeks to connect the human being with the great laws of the universe, the great laws of the cosmos. The deepest impulses of spiritual science will be understood in the true sense of the word only when people realize how extensively we are actually searching for the connection between human beings and the great transcendental laws of the universe.”  Rudolf Steiner

"I believe that scientific knowledge has fractal properties, that no matter how much we learn, whatever is left, however small it may seem, is just as infinitely complex as the whole was to start with. That, I think, is the secret of the Universe." Isaac Asimov 

“Every moment is of infinite value, for it is the representation of a whole eternity.” - Goethe 

“The Universe designs itself … every particle, every molecule, every organism, every celestial body in the Cosmos, exists and develops in the context of every other.” – Paul Harrison

"The whole universe is based on rhythms. Everything happens in circles, in spirals." – John Hartford

"That which is now called natural philosophy, embracing the whole circle of science, is the study of the works of God and is the true theology. As to the theology that is now studied in its place, it is the study of human opinions and of human fancies concerning God." –Thomas Paine 

"The cosmological picture that emerges--a map in time as well as in space--is not what most of us expected. It offers a new perspective on how a single "genesis event" created billions of galaxies, black holes, stars, and planets, and how atoms have been assembled--here on Earth, and perhaps other worlds--into living beings intricate enough to ponder their origins. There are deep connections between stars and atoms, between the cosmos and the microworld. . . . Our emergence and survival depend on very special "tuning" of the cosmos--a cosmos that may be even vaster than the universe that we can actual see." —  Martin Rees 

"To the eyes of a human of imagination, nature is imagination itself" —  William Blake 

“What makes every real work of art of interest is that it reproduces the mystery of Creation which operates in the Microcosm as in the Macrocosm, in Man as in the Universe.” — Edouard Schure 




Thursday, September 8, 2022



12” x 12”, oil on canvas, 2022

A single leaf is more intelligent than all the worlds computers. Machines need a maker, parts, and a plan. The leaf self-organizes and grows it’s own design, parts, and functions from light.

"Both leaves and eyes have learned how to make sense of photons of light." 
— Simon G. Powell
"The world is not a machine. Everything in it is force, life, thought."  Leibniz
“If you can paint one leaf, you can paint the 
world.” — John Ruskin  

Photomorphogenesis in Deep Dream AI .. 

Artwork made by human intelligence, about natures intelligence, interpreted by artificial intelligence .. 
 * * *

Tuesday, June 21, 2022

The Integratron Root Square


 “The Integratron Root Square
6” x 6”, acrylic on canvas, 2022

* * *
“Geometry is knowledge that appears to be produced by human beings, yet whose meaning is totally independent of them." 
 Rudolf Steiner

In the process of geometrically exploring the relationships between the first three root ratios (2, 3, 5) and finding a way to integrate them visually in a meaningful way into a kind of symbol, or put them in a relationship that could be simplified or contained within a square, I discovered this overall way of integrating the three roots, what I am calling the "Integratron Root Square."

What I'm interested in are how these fundamental root relationships with the 2, 3 & 5, and their shapes (the square, triangle, and pentagon), are interconnected and inter-generating universal constants. It's hard to imagine them as separate functions or laws, especially when the certain extended geometrical properties of lines of different ratios or grid patterns or circles overlap almost magically to create just the exact different ratios, points, and angles needed, and integrated in perfect alignment. 

“The dynamics generated within the three primary shapes are illustrative of the self-organizing forces of nature.” - Jonathan Quintin

These three roots, the square root (2), cube root (3) and phi (5) encompass both even & odd numbers, with 5 being an integration of both, altogether form a trinity of generative principles or roots (Jonathan Quintin). Phi or 5 has the quality of something extra it seems, it has the uneven/indeterminate generative/emergent element or creative and self-balancing dynamic seen by living systems, a self-referencing feedback property, or a "dynamic fracticality", in relation to the Fibonacci sequence, seen in both animate and inanimate pattern formations in nature.

“You will know, as far as it is allowed to a mortal, that nature is from all points of view similar to itself.” - Pythagorus 

The Pythagorean Trinity, Fibonacci Sequence, and Creation Geometry

To me this trinity of generative root ratios seems to be connected to what is called the Pythagorean Trinity (Ken Wheeler), and the relationships between the first five numbers in the Fibonacci sequence, (1, 1, 2, 3, 5). In the metaphysics of the Pythagorean Trinity, the One is considered ultimately transcendent and absolute, beyond any representation, but is represented as an indefinite dyad (1,1), as an inseparable transcendent principle and manifest attribute of the One, that makes up the first two numbers of the Fibonacci sequence and the first part of the Pythagorean Trinity. The first 1 represents the intrinsic transcendent in principle, and the second 1 its inseparable extrinsic attribute.  Thinking about this, the two initial overlapping circles of the vesica piscis come to mind as a kind of visual, with both representing a "one."

The golden ratio emerges from the two systems of geometry generated out of the vesica pisces, the ad triangulum and the ad quadratum (root 3 and root 2), and these two geometries were generated from two perfect spheres or circles or infinities or "ones" overlapping at their midpoints. So two circles (pi/infinities) overlap to create root 2 & root 3, which then those geometries overlap to create root 5 (phi/golden ratio). This relationship between the square and cube,  (2, 3), is the second part of the Pythagorean Trinity, and represents the emergence of the principle of duality and its relationship with the One, which links back and creates a trinity, representing the manifest universe and all things in 3 dimensions.

The third part of the Pythagorean Trinity are the relationships between 3 and 5, the cube and golden ratio/phi, the trinity and life (being/ontology), and is the final integration or "consubstantiation" of the first two parts of the trinity (Spirit-Matter/One-Many/Transcendent-Immanent).

The feedback of the Fibonacci sequence seen in this way is the feedback of life or phi with the continuum of the present moment, the One, or the "irreducible One" as R. A. Schwaller de Lubicz phrased it; the self-balancing and self-organizing and spiraling of polarities and dualities back into the constant creation of the present moment, the infinite one-continuum of the eternal ever-present, with its many uncertain and emergent outcomes, bifurcations, and growths. 

In this way, geometry is an interactive and deductive metaphysical tool we can use for understanding and discovering the inner "mechanics" of the universe, its generative archetypal constants, and the ultimate source of the transcendent and its connection to all things.

This is the metaphysics of the origin of process, the origin of order, and the origin of origin; the fact that all logic, order, and rationality in the universe originates from numbers and shapes with irrational roots and principles is quite the curious mathematical mystery.

“The compass is the most important scientific instrument that humanity ever invented.”  Keith Critchlow

"The study of geometry is a meditation on the harmony of the cosmic order."  Pythagoras

“Details make perfection, and perfection is not a detail.” ― Leonardo Da Vinci

Initial study for Integratron, compass & pencil

Extended circles & lines

Fractally embedded root ratios


"I have a distinct feeling that number is a key to the mystery, since it is just as much discovered as it is invented. It is quantity as well as meaning." —Carl Jung

"Number thereby throws a bridge across the gap between the physically knowable and the imaginary. In this manner it operates as a still largely unexplored mid-point between myth (the psychic) and reality (the physical), at the same time both quantitative and qualitative, representational and irrepresentational." —Marie-Louise von Franz

"It may well be the most primitive element of order in the human mind... thus we define number psychologically as an archetype of order which has become conscious." — Carl Jung 

Alternative study with root ratios and 
pentagonal geometry (Albrecht Dürer method)

The three roots overlaid and aligned with Leonardo da Vinci's Vitruvian Man geometry

"Unity is plural and, at minimum, is two." — Buckminster Fuller

“One becomes two, two becomes three, and out of the third comes the one as the fourth.”  Maria Prophetissa

"The one engenders engenders the two, the two engenders the three and the three engenders all things."  Tao te Ching 

"All the effects of nature are only the mathematical consequences of a small number of immutable laws."  Pierre Simon de Laplace

"Where there is matter, there is geometry."  Johannes Kepler

"The harmony of the world is made manifest in Form and Number."  Sir D'Arcy Wentworth Thompson

"Geometry purifies the eye of the soul, since it is by it alone that we contemplate the truth."  Plato
“There are fractal codes containing the laws of creation and the more we understand these laws the more we can apply the harmony that is apparent in nature as a more powerful force in our own lives. There is truth and purity in natural things and our contact with them nourishes the soul and illumines the mind.” - Jonathan Quintin 
"Music is the arithmetic of sounds, as optics is the geometry of light." — Claude Debussy 
“With light poise and counterpoise, Nature oscillates within her prescribed limits, yet thus arise all the varieties and conditions of the phenomena which are presented to us in space and time.”  Goethe