Fractal Artwork




Sacred geometry of the Valentine heart

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I am an atheist but I deeply appreciate the teachings and inspiration of various religious traditions. Although this article talks about God, I use the term only because it's easier than constantly saying "the awesome mystery of nature or science." I also use the word "God" as the traditional placeholder for that which is too sacred to be named.

My story is about the way wise people in the forgotten past may have tried to understand and represent the relationships between man, woman and God, their sacred source.1

Let's start with the idea that the first people to believe in a single source of everything believed that God is infinite and perfect. God is the ONE. And let's assume there were ancient mathematicians trying to understand the world using algebra and geometry. So, if they wanted to diagram the idea of God, they used the symbol "1".


Of course, the earliest people didn't start off thinking the symbol meant God. They just needed a quick symbol for counting things and there isn't anything much simpler than a vertical dash. When the wise ones finally got around to thinking about the meaning of life and its source, they borrowed the symbol for one since it was ubiquitous and helpful, which is a kind of definition for God.

So, they had a simple, powerful symbol to express the idea of a single God or source. But how were they to represent man and woman? Well, if God is 1, then man and woman must be symbolized as something less than God. And they must be represented as almost the same but complementary to each other.

manThe wise ones trying to figure this out looked around at nature and at art and they noticed there was a kind of rule for creating beauty. It didn't matter if the beauty was created by God or by humans. They saw this rule in the relative sizes of plant parts. DaVinci saw it in the proportions of the human body. Builders used it to create beautiful cathedrals. The rule is introduced to every beginning artist as the Golden Ratio or Phi.plant

Because this ratio seemed very mystical and powerful to the ancients, they decided it could be useful in representing a human when compared to God. Assuming those on earth are created in the image of God, the symbol for a human would be the same as for God but much smaller, as in the proportion of the Golden Ratio.

stemThe symbol for God, however, is vertical, as in the spirit reaching for heaven or flowers growing towards the sun . But the symbol for humans couldn't be the same because the wise ones recognized that humans are not perfect like God. Not everyone is on the vertical path to heaven.

Plus women and men are, in fact, opposites in matters of regeneration.

So the wise ones came up with this: angled dashes to symbolize men and women using the angle halfway between the vertical and the horizontal. And they stuck those symbols on top of the God symbol. In accordance with the Golden Ratio, the human symbols are smaller than the God symbol The result is a mystical "Y".Y

Wonderful! The wise ones had a new symbol to represent God's relationship with man and woman. What next? Well, children of course.

Looking at nature again, the wise ones noticed that God is ruthlessly efficient. If some strategy for growing or reproducing life works, then that same successful formula is applied over and over again. Today we call this the science of algorithms but in those days it was simply called holy.


With this in mind, the wise ones took the algorithm they used to represent man and woman and the relationship with the Sacred One, and they repeated it to represent the next generation of man and woman as well. The same Golden Ration of size and the same angle of divergence from the source. They repeated this formula again for the next generation. And again and again for each subsequent generation.



In nature and science, when the same formula or algorithm is applied to the results of the previous generation, we call it "recursion." At least that's the name we give it today. In the old days it was called sacred or magic because the results were so often amazingly beautiful - like a blessing from heaven. The symbols remain to this day and they're still important to us even though we have forgotten where they came from.

heartIt's rather sad that many of us feel so superior when looking at ancient or traditional beliefs. With our "modern" pride in science and technology, we dismiss as primitive superstition the connection that old traditions honor between learning and "spirit".

But what have we got to show for it? A chaos of competing desires, a vulnerability to the greed of those fixated on short-term goals, information overload and a pervasive lack of meaning.

Don`t get me wrong and jump to the conclusion that I'm saying "everything old is good". This is not a black and white issue of east versus west, modern versus ancient or religious versus atheist. The thinking and symbols that gave rise to the Valentine image were about "AND." The mystical interpretation could be, "In order to find meaning in relationship, embrace both sides equally and consider the source and the product i.e. Man AND woman AND children AND God.

But symbols are just symbols - they have no meaning beyond what we give them. The angled dashes of man AND woman could represent east AND west, or modern AND ancient, or religious AND atheist. Regardless of the meaning we attach, though, it's a geometry that's helpful for thinking about relationships.

Follow up

When I first came up with the "Valentine heart" many years ago, I did some research on the net but couldn't find anything to support, disprove or add to the story. I should have done that again before posting here. New information about ancient sources has sprung up.

The structure of the tree can actually be traced back to Pythagoras, although with differences in terms of proportions. I should have remembered the similarities from my grade school geometry introduction to right angles. Here is the Wikipedia entry:

A rather verbose orientation to Pythagoras and his sacred geometry can be found here:

Modern reworkings of the Pythagoras Tree can be found on the web using the search term: fractal tree. Some of the most interesting are on Flickr.

The only application of the Golden Ratio to the Pythagoras Tree I found was an intriguing sculpture done in 2008 by Mark Wallinger for Magdalen College in the UK: . The Golden Ratio is used in the segment lengths but not in the height and width of each segment.