The construction needs a compass and nothing else. Draw a circle. Put the compass point anywhere on its circumference and, without changing the radius, draw a second circle. The two overlap in the pointed almond called the vesica piscis. Now step the compass point around the first circle, each time placing it where the last circle crossed, and after six moves you arrive exactly back at the start. Six circles close around a seventh.
That the radius divides its own circumference into exactly six parts is not a coincidence or a mystery. The chord subtending sixty degrees is equal to the radius, which is the same fact that makes the regular hexagon the easiest polygon to construct and the reason six-fold symmetry turns up wherever equal circles are packed.
What the figure contains follows from that. The six outer centres are the vertices of a regular hexagon. Joining alternate ones gives two overlapping equilateral triangles, the hexagram. The twelve outer arcs form a six-petalled rosette, a shape carved on chests, beams, gravestones and church fittings across Europe and the Near East, usually under local names having nothing to do with sacred geometry. Continuing the same stepping outward, instead of stopping at seven, produces the wider lattice now called the Flower of Life.
Because the construction is self-terminating and self-checking, if the seventh circle does not land back on the first, the compass slipped, it is among the first exercises given to anyone learning compass work, and has been for a very long time. Much of the pattern's distribution across unconnected cultures is explained by that alone. It is what a compass or a pair of dividers does most naturally, and it needs no transmission of doctrine to appear in two places at once.