Mormonism and the Fractal Lineage of Gods

Composite image sourced here and here

In the symbolic language of Mormonism, the circle indicates eternity. This symbolism was introduced by Joseph Smith in his expounding on eternity's nature. He used the most common symbol he had at his disposal. Prophets take eternal concepts which are beyond anything we can completely express and communicate them using familiar symbols or objects. This is semiological transmission with its encoding and decoding. And as Mormonism promotes the idea of continuous revelation of further truths, I believe the symbol system of fractals, which has come to us after the life of Joseph Smith, can be welcomed to provide clearer resolution of Mormon truths surrounding creation, cosmology, ontology, and aesthetics.

As a quick primer, I’m using the term “man” or “men” to have the meaning “one who has intelligence”, similar to RenĂ© Descartes’ rational animal, which I believe is true to the intent of the authors and which I think is appropriate from a transhumanist perspective.

The symbolism of a circle (also shared in other world-views) was emphasized by Joseph Smith in 1844:
A ring belonging to Smith
likely worn by him in 1844

“… I take my ring from my finger and liken it unto the mind of man — the immortal part, because it had no beginning. Suppose you cut it in two; then it has a beginning and an end; but join it again, and it continues one eternal round. So with the spirit of man."

--Joseph Smith on Apr. 7, 1844, in Nauvoo, Illinois

It's a simple, yet powerful symbol that causes the mind to think beyond linear, finite time in nature and instead ponder on the nature of nature itself. What are the attributes of the eternities that underpin existence? And how does consciousness fit into that context?

Here, Mormonism deviates from traditional Christianity. It denies the doctrine of creation ex nihilo; thus affirming the eternal nature of the elements. It rejects fundamental immateriality anchoring all that is to material expression -- though it allows for more exotic forms of matter. And it exalts the mind of man to the same eternities of God; making our spirits co-existent with God.

Out of this fertile philosophical soil comes music and poetry written in the language of an LDS hymn:

"If you could hie to Kolob In the twinkling of an eye,
And then continue onward With that same speed to fly,
Do you think that you could ever, Through all eternity,
Find out the generation Where Gods began to be? ...

"Or see the grand beginning, Where space did not extend?
Or view the last creation, Where Gods and matter end?
Methinks the Spirit whispers, "No man has found pure space,
Nor seen the outside curtains, Where nothing has a place."

Later Lorenzo Snow, who knew Joseph Smith personally, echoed this sentiment as he coined a famous Mormon couplet:

"As man now is, God once was; as God is now man may be."

So while Christianity sees a causal arc from God to man, Mormonism completes that arc with a causal arc from man to God (a very transhumanist ideal). Woven throughout Mormonism is this notion of an eternal continuum of man and God: that we are of the same stuff of God, though at a more primitive stage of maturation. And it's in this framework that the symbol of God as our Father takes root. There's a filiation with God, as Joseph Smith explained:

"God himself, finding he was in the midst of spirits and glory, because he was more intelligent, saw proper to institute laws whereby the rest could have a privilege to advance like himself. The relationship we have with God places us in a situation to advance in knowledge. He has power to institute laws to instruct the weaker intelligences, that they may be exalted with himself, so that they might have one glory upon another, and all that knowledge, power, glory, and intelligence, which is requisite in order to save them in the world of spirits."

Note the language used here: God discovered our spirits, rather than invented them. This reminds me of the sentiment Arthur C. Clarke expressed about "the first born" in 3001 a Space Odyssey:

"... [since] in all the Galaxy, they had found nothing more precious than mind, they encouraged its dawning everywhere. They became farmers in the fields of stars."

This, to me, really illustrates the character and inquisitiveness of the Mormon faith and tradition. And I believe fractals provide a richer set of tools and symbols to better grasp and explore the Mormon picture of eternities usually symbolized as a circle.


Mandelbrot-Set Fractal

It’s important to understand the role and limits of symbolic language in revealing truths. As William James puts it so succinctly:

"Religious language clothes itself in such poor symbols as our life affords."

Joseph Smith used the best symbol he had at his disposal. Some 30 years after Joseph Smith taught the principles above, Karl Weierstrass developed the first models of fractals drawing upon Leibniz's "self-similar" geometry. The field of fractals progressed, creating (or perhaps discovering) increasingly intricate, complex, and strikingly beautiful shapes and patterns. And it hasn't been until the computer revolution that these fractals have been able to be visualized. This work was pioneered by Benoit Mandelbrot with his famously discovered Mandelbrot set.

Mormonism's ontology and views on salvation are amplified by the semantics offered by fractals. Beyond the symbol of an eternal circle, the lineage and destiny of mankind and godhood can be understood as a fractal progression. Among the attributes fractals have are:
  • Self-similarity: the shape contains repeating elements and patterns but can also have infinite variety.
  • Everywhere continuous but nowhere differentiable: following the limit of fractal functions, shapes drawn by fractals are continuous (natura non facit saltus), but paradoxically often don't have derivatives at any particular point.
  • Expressed as simple iterative/recursive functions: the equations which describe fractals are self-referential and surprisingly simple.
  • Aesthetic quality: While not a mathematical attribute, the endless aesthetic quality of fractals is one of it's most striking features.
Mormonism wouldn't be the first to express a tinge of spirituality in regards to fractals. Michael Barnsley who pioneered fractal compression algorithms, expressed this belief:

"Fractals are how God created a system which gave us free will. It's the most brilliant maneuver in the universe -- to create something in which everything is free." (1)

And Arthur C. Clarke mused on whether fractals might point to something more fundamental to our consciousness and psyche:

"Carl Gustav Jung would have been surprised and delighted to know that the computer revolution, which beginning he just lived to see, would give new impetus to his theory of collective unconscious: the idea that there's a well of consciousness compounded of primordial, universal images which we all share--the substructure, or background, of awareness. The mind clearly finds resonances in the Mandelbrot-set. But there are other wider implications too. [Fractal] math offers new insights into the way the universe works, how much of life is determined, and how much is due to chance." (1)

3-dimensional fractal source


Mormonism declares that “[God] has a body of flesh and bones as tangible as man’s" (D&C 130:22) and "God himself was once as we are now, and is an exalted man, and sits enthroned in yonder heavens!" (Joseph from the 1844 discourse cited above). Mormonism shares the broader Christian sentiment of man being made in the image of God, but goes further in pointing out how God contains the image of man. The Mormon temple experience underscores how the nature and purpose of this life is an eternal pattern which has been applied before. And Mormonism's doctrine of divinization arcs back towards this kind of mortal existence with the divinized "[instituting] laws whereby the rest could have a privilege to advance like [themselves]"; acting as gods in the goal of further exalting infinitely more co-existent spirits (monolatrism or even elements of apeirotheism).

Here, the symbol of a circle may be too simple. While Mormon cosmology may be compatible with self-similar ideas like infinite return, personal identity and progress is not reversed and the universe does not merely play out the exact same scene. Spirits which succeed in progressing inside the creations of gods then themselves become gods -- perhaps even participating in the authoring of new fractal expressions of creation and exaltation. But infinite, divine variety and individual agency of pre and post exalted beings is maintained. This would result in an infinite variation around the laws of godhood -- an idea better expressed as a fractal.

This infinite variation appears in Mormon scriptural language from creation accounts. In the Book of Moses, God explains the limited scope of scripture in relation to the infinities of His creations:

"But only an account of this earth, and the inhabitants thereof, give I unto you. For behold, there are many worlds that have passed away by the word of my power. And there are many that now stand, and innumerable are they unto man; but all things are numbered unto me, for they are mine and I know them."

This strikingly non-anthropocentric perspective dethrones mankind from notions of being the apex of existence. That while the filial relationship, co-eternality, and continuum between man and God strenuously orients God towards us, mankind is not an end but another iteration or generation in this eternal fractal. God sees His own past as well as His future in us; not dissimilar from the relationship a parent has with their children. Our created environment, or indeed environments that we in turn create, are a variation on this eternal pattern which has played and will play out with infinite variation through times and creations.

An interesting note here is that fractals are naturally occurring phenomenon. Mandelbrot expands on this in his book "The Fractal Geometry of Nature". And fractals have since become useful tools in things such as our increasingly realistic simulated environments, understanding symmetries in genomes, and improvements in telecommunications.

Recent ideas about consciousness have turned towards self-referential definitions, leading Douglas Hofstader to note in his book "I Am a Strange Loop" that:

"In the end, we are self-perceiving, self-inventing, locked-in mirages that are little miracles of self-reference."

This universality of fractals both in our real and simulated environments has strong implications for the simulation hypothesis. And the amplification of Mormon cosmological and ontological beliefs by fractal symbolism creates a fascinating intersection between creation, simulation, consciousness, and God.

Fractal generated using the distributed, fractal-generating, peer-to-peer network ElectricSheep - (source)

Everywhere continuous but nowhere differentiable

Mormonism defines eternal progress as "line upon line, precept upon precept, here a little and there a little". This echoes the principle of natura non facit saltus which was used by Leibniz and Newton as they independently invented calculus: that progress or change in nature is usually made by small almost imperceptible changes. This sentiment is also expressed elsewhere in Mormon scripture: "by small and simple things are great things brought to pass". And Joseph Smith taught (2):

"... we consider that [salvation] is a station to which no man ever arrived in a moment: he must have been instructed in the government and laws of that kingdom by proper degrees, until his mind is capable in some measure of comprehending the propriety, justice, equality, and consistency of the same.”

From a transhumanist or futurist perspective, Mormonism is capable of projecting through models like Kardashev Scales or Ray Kurzweil's epochs of evolution (I expand on that here). As we go from “a small capacity to a great one”, we can trust in our potential to progress into post humanity and beyond. John A. Widtsoe described a role that evolution plays in this process:

“Under the law of evolution, man’s organization will become more and more complex. That is, he will increase in his power of using intelligence until in time, he will develop so far that, in comparison with his present state, he will be a God.” (3)

Even God became God through this process of continuous progress and change. The New God Argument outlines some of the profound theological and philosophical implications of this kind of post-human progress.

Expressed as simple iterative/recursive functions

Fractal equation for the Mandelbrot Set

One of the amazing aspects of fractals is that their infinite diversity and complexity are expressed as remarkably simple equations. Mormonism strongly infers that God is not only the author of laws but governs Himself according to eternal law (source).

“All kingdoms have a law given; And there are many kingdoms; for there is no space in the which there is no kingdom; and there is no kingdom in which there is no space, either a greater or a lesser kingdom.”

Perhaps this fractal of godhood is expressed by some finite set of eternal laws out of which emerges infinite and recursive variety of mind and creation. And perhaps tools such as science and prophecy are capable of revealing these laws to us. Mormonism's fundamental laws anchor to a process of faith, repentance, ritual, and revelation -- all in the framework of moral agency and centered on Christ.

This creates very strenuous and awe-inspired attitudes towards what it is, exactly, that God is accomplishing with us by introducing us to these eternal laws. It breathes new life into scripture and the title Law-giver. Did he invent these laws? Or was it through His imbibing these laws that He became a God? Mormonism provides a mixed picture here with some laws treated as immutable yet God also having "power to institute laws" (from the Joseph Smith quote above).

This all comes back to the "man-God" continuum explained above. From a fractal perspective, here we are on the edge of some infinitely small arc in some larger curve which is on a leg the juts out from a larger arc, ad infinitum. The structures, patterns, and contours are familiar and have been playing out over infinite eternities and iterations. God sees in us the ability to continue the growth of this divine fractal onwards forever bringing with us the unique and co-eternal diversity and identity only we possess (our uncreated or uncreatable essence). We stand between infinities, and God is fully invested in our exploring the continuation of the fractal pattern which has brought Him to where He is. He guides us to escape the dark, destructive, void, and terminus edges of that fractal that we would wander into if left to our own devices -- even when that guidance requires significant sacrifice on His part.

Aesthetic Quality

Variation on a Julian fractal (source)

Fractal aesthetics and theological aesthetics have an interesting intersection here. Arthur C. Clarke made this observation:

"Why do these strange patterns have such an appeal? Obviously, they trigger some kind of resonance in the mind. Indeed, the Mandelbrot set does seem to contain an enormous amount of mandalas or symbols. And in ecclesiastical design such as stain glass windows, particularly in Islamic art, you can find many echoes of the Mandelbrot set centuries before it was discovered." (1)

The Mormon temple ritual and aesthetic has profound infinite, self-referential qualities. Ritual in general is cyclic and self-referential. As the participant performs and re-performs the ritual, new interpretations and patterns continuously unfold. Layering on top of this, the Mormon temple aesthetic folds this ritual back onto the self-referential expression of genealogies. This allows the power of the symbolism and ritual to resonate and echo across the generations of mankind both forward and backwards in time. This creates a kind of universal, familial, exalting mandala.

Mormon cosmology, ontology, and symbolism provide a rich foundation where diversity in discipleship can be infinite in variety. Elder Uchtdorf recently explained this principle:

"But while the Atonement is meant to help us all become more like Christ, it is not meant to make us all the same. Sometimes we confuse differences in personality with sin. We can even make the mistake of thinking that because someone is different from us, it must mean they are not pleasing to God. This line of thinking leads some to believe that the Church wants to create every member from a single mold — that each one should look, feel, think, and behave like every other. This would contradict the genius of God ...

"As disciples of Jesus Christ, we are united in our testimony of the restored gospel and our commitment to keep God’s commandments. But we are diverse in our cultural, social, and political preferences. The Church thrives when we take advantage of this diversity and encourage each other to develop and use our talents to lift and strengthen our fellow disciples."

While things like "[unity] in testimony" and "commitment to keep God's commandments" are likely a core part of a Mormon fractal expression, "moral agency" and individual "spiritual identity" are what allow the flourishing of infinite variety that gives Mormonism its aesthetic quality.

Freeman Dyson, in his book Infinite in All Directions, puts it this way:

“Diversity is for me the chief source of beauty and value, in the natural universe around us, in the governance of human societies, and in the depths of our individual souls. The profusion of stars and galaxies in our skies, the profusion of bugs and beetles in our gardens, and the profusion of human genius in our arts and sciences, all proclaim that God loves diversity. Diversity is the spice of life, and the prevalence of evil in our world is the price we pay for diversity."


Fractal geometry provides a compelling set of symbols to better understand and explore the Mormon aesthetics of ontology, cosmology, and ritual. Indeed, the language of Mormonism is rich with fractal symbolism: man-God continuum, co-eternal ontology and identity, line upon line, generations of gods, infinite variety, trans-generational salvation, rich repeating temple symbolism and ritual, many degrees of salvation, etc. Transhumanism fits nicely inside this framework as it seeks to bridge human and post-human realities — often by leveraging feedback loops between us, our tools, and our environments. Mormonism also has built into its foundations the idea of continuous revelation: that additional modalities, laws, truths, and symbols to understand, re-contextualize, and express our faith can be expected and even celebrated. And as the symbols used in Mormonism's founding are reflected upon in relation to the truths they signify, the additional focus and resolution that a framework like fractal geometry provides can serve to greater amplify those founding messages and truths.


(1) - Source: "Fractals - The Colors of Infinity"

(2) - Teachings of the Prophet Joseph Smith, p. 51

(3) - John A. Widtsoe's 'Joseph Smith as a Scientist', p.129