Technique · Geometry
Space colonisation
Branches grow toward scattered attractors and fill a shape: a root ball, a canopy, leaf veins, or crowds of competing neurons.
Space colonisation is drawn geometry, rebuilt as it changes. 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
- Veins form in a leaf where the plant hormone auxin flows toward the stem, and a flowing channel widens, which draws in more flow.
- Roots steer toward moisture: the tip senses a gradient and grows along it, a response called hydrotropism.
- The space colonisation algorithm was published by Adam Runions, Brendan Lane and Przemyslaw Prusinkiewicz in 2007, adapting their earlier model of how the veins of a leaf form.
- The pipe model, proposed in 1964, says a branch is as thick as the leaves it feeds; the thickness here follows it.
The mathematics
- At each step a tip turns toward the average of the unit vectors pointing to the attractors that chose it, then moves a fixed distance.
- An attractor is deleted once a branch comes within 0.012 of it, so growth stops exactly where the space has been filled.
- Every attractor belongs to its nearest branch, which is a Voronoi partition that is recomputed as the tree grows.
In art
- Skeleton leaves, with the soft tissue rotted away to show the veins, were a Victorian craft.
- Cajal drew neurons as trees, and later artists have drawn trees as neurons: the likeness runs both ways.
More ways to use it
Related techniques
L-system · Diffusion-limited aggregation · Flow ribbons · Ridgelines · Curve families · Streamlines · Paint strokes · Stipple and Delaunay portrait