The Flower of Life
Nineteen gold circles, all the same size, each one centred where earlier circles cross: this is the Flower of Life, drawn the way it can be drawn by hand, with a compass that is never reset. The menu walks through the other figures that modern sacred geometry books build from the same grid, from the seven circles of the Seed of Life to Metatron's Cube, whose 78 lines join 13 points in every possible way.
| Flower of Life | 19 circles |
|---|---|
| Seed and Egg of Life | 7 circles each |
| Fruit of Life | 13 circles |
| Metatron's Cube | 78 lines |
What you are looking at
While the figure builds, the compass needle sits on a centre and the pencil sweeps a full circle around it. Every new centre is a point where two circles already on the page cross, so the whole figure needs only a compass held at one setting.
The Flower of Life is 19 circles: one in the middle, six around it and twelve around those, inside a bounding circle three times as wide. Each circle passes through the centres of the circles beside it, which is what makes the overlaps into petals that meet at every centre.
The other figures come from the same grid. The Seed of Life is the first seven circles, the middle one passing through all six other centres. The Egg of Life, as it is usually drawn, is seven circles that touch without overlapping, two grid steps apart. The Fruit of Life is thirteen such touching circles along six rays. Metatron's Cube joins the 13 Fruit centres, every pair of them, with 78 straight lines. The faint circles underneath the Egg and the Fruit are the grid they are picked from.
The math
The centres form a hexagonal lattice: every point is some number of steps to the right plus some number of steps along a line at 60 degrees, each step exactly one radius long. Each point has six neighbours one step away, and the squared distance between any two points is a whole number. A ring k steps out holds 6k points, so the Flower is 1 + 6 + 12 = 19 circles, and its outer circles reach exactly 3 radii from the centre.
Metatron's Cube has 13 points, and 13 points can be joined in 13 x 12 / 2 = 78 ways. It is often said to contain all five Platonic solids. Three of them are there exactly, as the shadow each solid casts when seen along one of its lines of three-fold symmetry, straight down a corner of the cube or the tetrahedron and straight onto a face of the octahedron: the cube is the inner hexagon with lines to the centre, the octahedron is the outer hexagon with its two large triangles (their sides are exactly the square root of 3 times the hexagon's sides, as in the real solid), and the tetrahedron is one large triangle with its peak at the centre. Choose them under Solids in the cube.
The other two, the icosahedron and the dodecahedron, are built on the golden ratio: the icosahedron seen straight onto a face, for instance, is two rings of points whose sizes are in the golden ratio. Every squared distance between the 13 points is a whole number, so no two lines in the figure can be in the golden ratio. Those two solids can only be approximated here, so they are not drawn.
How it is computed
Every centre is an exact point of the lattice, and every circle has radius 1. The circles are drawn ring by ring, in an order where each new centre already lies on two circles drawn before it, and the tests check that for every circle. Metatron's Cube adds the 78 lines after its 13 circles, and the highlighted solids use only those 13 points. Nothing in the picture is eyeballed or approximated.
The overlapping-circle pattern is old: it turns up in Roman mosaics, in medieval decoration and in Leonardo da Vinci's notebooks. The names Seed, Egg and Fruit of Life and Metatron's Cube, and the meanings given to them, come from modern writing on sacred geometry and are a tradition, not a property of the circles.
Questions
Is the Flower of Life ancient?
The pattern of overlapping circles is old and widespread, from Roman mosaics to Leonardo da Vinci's notebooks. The name Flower of Life and the set of related figures shown here come from modern sacred geometry writing, which also gives them spiritual meanings. Those meanings belong to that tradition; the geometry is the same either way.
Does Metatron's Cube really contain all five Platonic solids?
Three of them, exactly: the tetrahedron, the cube and the octahedron appear as their true outlines, seen straight down a corner of the cube or the tetrahedron and straight onto a face of the octahedron, using only the figure's 13 points. The icosahedron and dodecahedron need lengths in the golden ratio, and no two lines in Metatron's Cube are in that ratio, so they can only be approximated.
Why do the circles line up so perfectly?
Because every centre is a point where earlier circles cross, at a distance of exactly one radius from its neighbours. A compass at one setting can only ever reach points of that hexagonal grid, so everything it draws fits together.