This definition explains how to create the famous Dragon Curve using RABBIT.

The Heighway dragon (also known as the Harter–Heighway dragon or the Jurassic Park dragon) was first investigated by NASA physicists John Heighway, Bruce Banks, and William Harter. It was described by Martin Gardner in his Scientific American column Mathematical Games in 1967. Many of its properties were first published by Chandler Davis and Donald Knuth. It appeared on the section title pages of the Michael Crichton novel Jurassic Park.

Recursive construction of the curve
It can be written as a Lindenmayer system with
angle 90°
initial string FX
string rewriting rules
X = X+YF+
Y = −FX−Y.

Source: Wikipedia

Get Dragon Curve Gh

Hilber Curve Definition using RABBIT.

A Hilbert curve (also known as a Hilbert space-filling curve) is a continuous fractal space-filling curve first described by the German mathematician David Hilbert in 1891,[1] as a variant of the space-filling curves discovered by Giuseppe Peano in 1890

Get 2D Hilbert Curve Gh Get 3D Hilbert Curve Gh

8 thoughts on “L-Systems: Space Filling Curves with Rabbit

  1. Valerie says:

    Very nice tutorial, thank you a lot! But can you tell me how to connect two rule panels to PR at the same time? When I’m trying to do so, one of them would disconnect…~ToT~

  2. gpgoel@gmail.com says:

    Hello this grasshopper definition for 2d hilber curve shows a straight line upon running.

  3. Lawrence Gomez says:

    Thank you for creating these clusters for Grasshopper, and introducing me to CA and L-systems! I’m coming from ecological design to CAD to this. Question: How can I produce F1 and Fr expressions in the algorithm?

  4. kemalardaalkin@gmail.com says:

    Does this have Mac compatibility or works in rhino 6 because I can’t figure out in both 🙁

  5. Morphocode says:

    Hi,
    we haven’t updated Rabbit in a while so it might not work with the latest versions of Rhino. You might have to use Rhino5 on windows to get it working.

    We would like to update the plug-in to make it compatible with the latest Rhino/GH (with Mac support), but at this time we don’t have an exact release date.

    Regards,
    Kiro

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