flower of life

the flower of life is a well-known, flower-like, geometric pattern that has been found in temples, manuscripts and pop culture for thousands of years. the pattern also plays a role in esotericism. we will leave all that aside at this point and concentrate on the simple construction of the geometric form, which is composed of several evenly distributed, overlapping circles.

The shape, perceived by many as harmoniously perfect, has sixfold symmetry and is known to many philosophers, architects and artists around the world. Their recursive construction process is particularly simple.

Draw a circle \(K_1\) with radius \(r>0\) around center \(m_1\ ) and a second circle \(K_2\ ) with radius \(r\ ) around center \(m_2 \in K_1\). All further circles \(K_n\ ) now follow the following property: They each have radius \(r\ ) and a center \(m_n\ ) at any intersection of the previous circles.

The degree \(g\) a pattern is called \( \text{round} \left( \frac{ max(\overline{m_n m_1})}{r} \right) -1\) . We only draw circles if \(\overline{m_n m_1} > g+1\) holds. Finally we enclose the pattern with a circle of radius \(r \cdot g\) around the center \(m_1\) . In the "strict" version of the Flower of Life, all circles with \(\text{round}\left( \overline{m_n m_1} \right) = g\) or \(\text{round} \left( \overline{m_n m_1} \right) = g-1\) only those circular arcs are drawn that are between their points of intersection with all circles \(K_k\) with \(\text{round} \left( \overline{m_k m_1} \right) = g-1\) or \(\text{round} \left( \overline{m_k m_1} \right) = g-2\) .

With SVG.js and some school trigonometry we construct a Flower of Life of any degree:

See the Pen Flower of Life by David Vielhuber (@vielhuber) on CodePen.