Technique · Fields
Linked rings
A tangle of pentagonal frames of square bars in rainbow colours, linked through one another and tumbling slowly in space.
Linked rings is a field drawn for every pixel by the graphics chip. Every piece on Synapse Drip is made from a recipe that layers techniques like this one, and you can change any of it in the Studio.
Good to know
- Interlocked frames like these recall the compound of five cubes, which fits inside a dodecahedron, and Escher's print Stars (1948), which shows interlocked polyhedra drifting in space.
- Mathematical sculptors such as Bathsheba Grossman and Helaman Ferguson make knots and linked forms in metal and stone, often from a single equation.
- A regular pentagon cannot tile the plane, but five-fold forms are everywhere in nature, in starfish, flowers and the twelve five-fold corners of many virus shells.
- Five-fold symmetry cannot tile a flat surface or occur in an ordinary crystal; it was a surprise when Dan Shechtman found it in an alloy in 1982, a discovery that won the Nobel Prize in Chemistry in 2011.
- In the Borromean rings, three rings are linked so that cutting any one frees the other two; the arrangement has been a symbol for centuries.
The mathematics
- The interior angle of a regular pentagon is 108 degrees, and the ratio of its diagonal to its side is the golden ratio, 1.618; each of the 12 frames has five such sides.
- The distance to a square bar is the largest of the absolute offsets in its two cross-section directions and beyond its ends, the max-norm, which is never larger than the true distance, so the march can never overshoot a bar.
- Sphere tracing, introduced by John Hart in 1989, moves each ray forward by the distance to the nearest surface, which is why a few dozen steps are enough to find any bar.
In art
- Colour wheels in rainbow order have been used to organise colour since Newton drew his in 1704.
- The square-cut bars give every face its own shade, the faceted look of early computer graphics, where flat shading was cheap and crisp.
More ways to use it
Related techniques
Nebula and stars · Liquid · Droplets · Network · Terrain and maps · Neuron · Order to chaos · Fractal tree