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Pure entertainment: click the "crawl" control button for 100 steps and study the movements of an artificial worm.

Contributed by: Karl Scherer (October 2011)
Open content licensed under CC BY-NC-SA



This is an application of the Mathematica built-in functions Tube and BSplineCurve. Some control points are provided and the curved tube will follow by bending gently.



Use this control to let the worm crawl 1, 10, 100, or 1000 steps.


This slider controls the thickness of the worm.


This slider selects the spline degree of the worm curve. The higher the degree, the smoother the curve.


This slider controls the agility of the worm. The higher the agility, the more bends it makes.


"light = Neutral/Automatic/None" are three lighting options.


Click this checkbox to show the coordinate axes.


Click this checkbox to show a 6×6 grid in the plane.


Click this checkbox to show a 6×6 gray square (the floor) in the plane.

"max height"

The worms stays in a box of size 12×12×(2×max height).

Hence the variable "max height" determines how far above or below the 12×12 floor grid the worm can venture.

"floor opacity"

This slider controls the opacity of the floor.

"worm", "floor", "bgr"

These controls select the colors of the worm, floor, and background.


The Demonstration runs faster if you unselect "floor" and "grid".

See also 3D Curve Constructor by the same author.

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