The Flower of Life is a well-known, flower-like, geometric pattern that has appeared in temples, manuscripts, and, more recently, in popular culture for thousands of years. The pattern also plays a role in esotericism. We will disregard all of that here and focus on the simple construction of the geometric form, which consists of several evenly spaced, 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 \(r>0\) centered at \(m_1\) and a second circle \(K_2\) with radius \(r\) centered at \(m_2 \in K_1\) . All further circles \(K_n\) now satisfy the following property: They each have radius \(r\) and a center \(m_n\) at any intersection point of the preceding 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.