Phyllotaxis, pushed pattern-forming fronts, and optimal packing.

Pattern formation in the wake of triggered pushed fronts

Pattern-forming fronts are often controlled by an external stimulus which progresses through a stable medium at a fixed speed, rendering it unstable in its wake. By controlling the speed of excitation, such stimuli, or “triggers,” can mediate pattern forming fronts which freely invade an unstable equilibrium and control which pattern is selected. In this work, we analytically and numerically st...

What a Sunflower Can Teach a Robot? - Efficient Robot Queuing by Reverse Phyllotaxis

We present a distributed multi-robot controller for forming spatially efficient queues of arbitrary numbers of robots. The method is formally analyzed and validated in a conventional robot simulation. This controller is based on sunflower phyllotaxis and inherits its efficient packing properties. Two measures of queue spatial efficiency are proposed and their upper bounds for the presented cont...

Do Fibonacci numbers reveal the involvement of geometrical imperatives or biological interactions in phyllotaxis?

Complex biological patterns are often governed by simple mathematical rules. A favourite botanical example is the apparent relationship between phyllotaxis (i.e. the arrangements of leaf homologues such as foliage leaves and floral organs on shoot axes) and the intriguing Fibonacci number sequence (1, 2, 3, 5, 8, 13 . . .). It is frequently alleged that leaf primordia adopt Fibonacci-related pa...

Inside dynamics of pulled and pushed fronts

We investigate the inside structure of one-dimensional reaction-diffusion traveling fronts. The reaction terms are of the monostable, bistable or ignition types. Assuming that the fronts are made of several components with identical diffusion and growth rates, we analyze the spreading properties of each component. In the monostable case, the fronts are classified as pulled or pushed ones, depen...

Phyllotaxis or the properties of spiral lattices. - II. Packing of circles along logarithmic spirals