This figure opens every part of the book, and it is borrowed. Borrowed things should be explained, so here is the explanation.
How it is drawn
Start with one circle. Put a second circle of the same size with its center anywhere on the first one's edge. Keep going around, and you will find there is room for exactly six — no more, no fewer, each one touching the center circle and both of its neighbors. Six is not a design choice. It is what the plane allows.
One. Then the seven the plane allows. Then nineteen, which is where we stop drawing — not where it stops.
Carry on and it tiles the whole surface, outward, forever, every new circle passing through the centers of six others. The version used here has nineteen, which is the count in the best-known ancient examples of it.
Where it comes from
The honest answer is that it comes from a great many places, that the sources disagree, and that the popular version of the story is tidier than the evidence supports.
The oldest securely dated examples are Assyrian, from the royal palaces of the seventh century BCE. Which palace and which king depends on which account you read, and the accounts do not agree with each other — one of the small warnings you get, early, that this is a subject where confident dates are cheap.
The famous examples are Egyptian, at Abydos: five patterns of nineteen overlapping circles, drawn in red ochre on granite columns, faint enough that they are easy to miss and easier to photograph badly. They are usually presented as thousands of years older than the Assyrian ones. They are probably not. The figure does not appear anywhere in the vocabulary of native Egyptian ornament, the patterns look like graffiti rather than architecture, and the most careful recent work puts them no earlier than 535 BCE and most likely somewhere between the second and fourth centuries CE — which would make them younger than the Assyrian examples by a thousand years, not older.
After that it is simply everywhere. Phoenician, Roman, Indian, Chinese, Islamic, medieval European. Leonardo worked through the figure and its geometry across pages of the Codex Atlanticus. Cultures that never met each other arrived at it independently, which is the most interesting fact about it and gets the least attention.
The name is modern. Nobody who made the ancient examples called it the Flower of Life; that phrase came into wide use through late-twentieth-century writing on sacred geometry, and it has stuck so thoroughly that the older, plainer description — an overlapping-circles grid — now sounds like the unusual one.
What we did not borrow
A large body of modern writing attaches specific metaphysical claims to this pattern: that it encodes creation, or consciousness, or a blueprint underlying matter.
This book makes none of those claims, and nothing in it depends on them. If you hold them, you are welcome here and this page is not an argument with you. It is only a disclosure, because a book that asks its readers to care about evidence should be clear about what it is importing along with a drawing.
We borrowed the geometry.
If that sounds like the smaller half, it is not.
Why this book uses it
Look at what the figure actually does.
Every circle in it is whole. Not one of them is a fragment, or a supporting element, or decoration around something more important. And every circle is also inside six others — overlapping them, sharing area with them, impossible to lift out without taking pieces of its neighbors with it.
There is no center. Cover any circle you like with your thumb and the drawing does not lose its middle; pick any other circle and the whole arrangement organizes itself around that one instead, and looks exactly the same. The figure has no privileged position in it, and no way to make one.
And the edge is not an edge. The boundary is where the drawing stopped, not where the pattern did. Nineteen circles is a decision about paper.
That is the book's argument, in a figure, before a word of it is read.
And it is not only a figure
Here is the part that decided it.
Circles packed this way — each one ringed by six — is the arrangement living things keep arriving at. It is the honeycomb. It is the array of lenses in a dragonfly's eye. It is what soap bubbles fall into when you crowd them onto a flat surface, and what cooling basalt cracks into at the Giant's Causeway, and what a raft of identical cells settles toward when it is pressed together with nothing else deciding the outcome.
They are not copying each other. There is no lineage running from a bee to a bubble to a column of volcanic rock.
They are all being pushed toward the same answer, because it is the best one available. Draw the boundaries between circles packed this way and you get hexagons — and in 1999 the mathematician Thomas Hales proved that hexagons divide a surface into equal areas using less total boundary than any other shape, regular or irregular. Nothing does it more cheaply. Nothing can.
So the ornament turns out to be a description.
Nobody who first drew it had proved anything. They drew it because it looked right. It took until 1999 to show why it is.