Hodograph Turtles

T. Ju and R. Goldman (USA)


turtle geometry, fractal, hodograph.


In classical turtle graphics a line is drawn to connect the tur tle's position vector before and after executing each FOR WARD command. A hodograph turtle shadows the clas sical turtle and draws a line connecting the classical tur tle's direction vector before and after executing each TURN command. Here we study examples of the hodograph tur tle in action along with several extensions. We show that some shapes are easier to generate using a hodograph tur tle instead of the classical turtle. More importantly, we can extract information about the program of the classical tur tle from the geometry generated by a hodograph turtle. We shall see that especially for complicated turtle paths such as fractals, the path of a hodograph turtle is often much sim pler and easier to understand than the path of the classical turtle. This simplicity reflects the simplicity of the under lying turtle program which is not always evident from the actual fractal path traversed by the classical turtle. We also show how to extend the power of the hodograph turtle so that the hodograph turtle can draw the same class of fractals as the classical turtle.

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