When I started making caterpillars 25 years ago I focused on the math for straight line 2D movement. Then I figured out the math for constant curvature terrain like circles, and then variable curvature terrain like the Woodpile. Recently I figured out the math for arbitrary curves in 3D space. In 2022 I made a series of about 12 animations using this new 3D math. To make this animation I first drew the tape measure and combination square. Then I put the drawing briefly in Blender to find a camera angle and a handful of 3D points that looked to be on the path I wanted the caterpillar to follow. Next, in python, I used those points to create a spline of the path and chose various parameters for the caterpillar and calculated the caterpillar’s position at any given moment in time. I also calculated the shape and intensity of the shadows. Then I multiplied everything by the perspective matrix to get screen coordinates and plotted the caterpillar and shadow using matplotlib in python.