Spiral Lattices Applet


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Some tips about this applet

This applet enables the exploration of all possible spiral lattices and their organization according to their divergence angles, expansion rate, and parastichy numbers. To see the relation between these three entities and visualize the spiral lattices, click the mouse in the Parameter Space. Move the mouse keeping the button pressed. To each point P of the parameter space corresponds a spiral lattice. The divergence angle of the lattice is given by the angle P makes with the x - axis, and expansion rate by the inverse of the distance from P to the center of the parameter space.

  • The option Parastichies  shows  the spirals that you may have perceived mentally by connecting the dots to their nearest neighbours.
  • The option Closest Points shows the 2 closest points to the blue point on the central circle (which represents potentially the newest primordia on the edge of the meristem).
  • The option Generative Spiral joins the points in order of increasing distance from the center. In a plant, this would retrace the chronology of the primordia formation.
  • The option Circle draws the circle centered at the blue point and passing through the second closest point to it. It enables one to visualize the changes of first and second closest points which determine entirely the changes in  numbers of parastichies.
  • The option Image shows the partition in the parameter space in regions where the number of parastichies are constant. If you follow the red paths starting from the center of the Parameter Space (the lattice will be distichous at first) with your mouse clicked on, you will see a succession of spiral lattices with Fibonacci phyllotaxis (count the number of spiral you see at the different stages, and note the angle towards which the paths lead you (about 137.5 and 222.5)).

When you are ready for more information about the program and its options, go to the step by step tutorial.