In this mind-bending short film, US designer John Edmark, a lecturer in mechanical engineering at Stanford University, uses 3D printing, the mathematics of the golden ratio and photography tricks to create moving symmetry – a bloom.
[The] animation effect is achieved by progressive rotations of the golden ratio, phi (ϕ). This is the same golden ratio applied in nature, seen in pinecones and sunflowers.
Edmark also uses a camera on an incredibly short shutter speed to mimic a stroke effect that you would find on a zoetrope.
The speed of the shutter occurs in concert with the bloom as it turns 137.5º (the angular version of phi).
Each bloom’s particular form and behavior is determined by a unique parametric seed called a phi-nome (/fī nōm/)
This reminds me of Kunstformen der Natur or Artforms in Nature by German naturalist and biologist Ernst Haeckel. In this classic book originally published in 1899, you can find all kinds of lithographs and watercolours of organisms.
The main over-riding principle that guided Haeckel was that each of these organisms displayed complexity and intricate symmetry. He loved to capture ammonites, boxfishes, jellyfish and micro-organisms for this reason, arranging them for maximum visual and aesthetic impact. I have written about Haeckel’s gorgeous book of treasures before in an article called Exquisite Marine Invertebrates of the 19th Century.