This applet demonstrates phyllotactic patterns as seen in plants like sunflowers, pineapples and coniferous trees. Phyllotactic patterns are an example of algorithmical forms in nature.

The formula for phyllotactic patterns is r=c*sqrt(n), d=n*137.5, where r is radius, c is a constant scaling factor, n is the number of the current seed (counting from the central seed as n=1) and d is angle. The rotation of each point by n*137.5 degrees causes phyllotactic spirals. The use of any other angle constant than 137.5 causes overlapping and non-optimal packing, although the patterns generated are not uninteresting from an aesthetic point of view.

The applet lets you experiment with setting the angle constant by clicking around in the image. Pressing "p" will toggle display of the current angle constant. There are three display modes: Circles, dots and lines. These can be used in any combination, circles being the default. Pressing 'c', 'd' and 'l' respectively will toggle these display modes. Experiment with viewing the pattern as dots to see the perfect packing or lines to see the points connected in the order they are placed.