Technique · Geometry
Curve families
One curve repeated with a little shrink, turn and drift each time: spirograph envelopes, shells, bow-ties and mandalas, as pen-plotter drawings.
Curve families 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
- A cardioid is the envelope of circles whose centres lie on a circle and which all pass through one fixed point of it; the same heart shape forms the main body of the Mandelbrot set.
- A rose curve r = cos(k theta) has k petals when k is odd and 2k petals when k is even.
- String art, or curve stitching, builds smooth curves from straight threads between points on two lines.
- The envelope of a family of curves is the shape they all touch; string art draws it with thread.
The mathematics
- Copy i is scaled by s^i, a geometric sequence, so the sequence of 120 copies settles toward a point.
In art
- Sol LeWitt's wall drawings, from 1968, are written instructions that anyone can carry out; a recipe here plays the same role.
- Islamic geometric ornament builds intricate rosettes from a circle, a compass and a straightedge.
More ways to use it
Related techniques
L-system · Space colonisation · Diffusion-limited aggregation · Flow ribbons · Ridgelines · Streamlines · Paint strokes · Stipple and Delaunay portrait