String Art with Computer Graphics

A gallery of computer-animated string art by Jason Schattman that can fold and twist on itself.  Wait for the explosion at the end! :) I coded the animations in Python.

You can interact with the program on repl.it at https://repl.it/@schattj/String-Art#m.... Try creating your own designs by adjusting the skip-rates and the values of a and b.

The first circular web, which has 80 "nails",  is made by stringing each nail to the one that's 20 nails away from it, counterclockwise. Thus, nail 1 connects to nail 21, nail 2 connects to nail 22, nail 3 to 23, and so on. This 20 is arbitrary. Skipping more than 20 results in a fatter web and a smaller circle in the middle.  Skipping less than 20 results in a thinner web but a larger circle.

The crescent-moon web is made by stringing nail 1 to nail 2 (skipping 1 nail), then 2 to 4 (skipping 2 nails), then 3 to 6 (skipping 3), then 4 to 8 (skipping 4), etc. In other words, the number of nails being skipped increases by 1 with each new string.  

To get the 3-knobbed web, the number of nails being skipped over by each new string increases by 3 each time: 1 to 2 (skipping 1), then 2 to 6 (skipping 4), then 3 to 10 (skipping 7), then 4 to 14 (skipping 10), etc.

A bit more detail for the mathematically inclined
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The twisted-up webs that unwind into a circle in the second half of the video are made by interpolating between a given Lissajous curve parametrized by (sin at, sin bt) and the circle, parametrized by (cos t, sin t). For example, to get a a figure-8 curve, set a = 1 and b = 2, resulting in the parametric curve (sin 2t, sin t).  25% of the way through that animation, the curve being drawn is (0.75 sin 2t + 0.25 sin t, 0.75 sin t + 0.25 sin t), so that the curve is a 75-25 "mix" of a figure-8 and a circle.  In the final figure (the one that explodes), the starting Lissajous curve is (sin 4t, sin t) (a = 4, b = 1)

Here are some other math animations from my channel
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On the beautiful geometry of imaginary numbers & complex functions (can be enjoyed even without knowing what that means)
Twisting the Plane with Complex Numbers

All 6 trig functions on the unit circle
All 6 Trig Functions on the Unit Circle

Mathematical art using the idea of epicycles
Amazing Epicycles

Optical illusions made using trigonometric functions
Optical Illusions

Fancy "card tricks" animated using mathematical pretzels (called Lissajous curves)
Video

Sound waves in an oval room:  
The Physics of Sound Waves in an Ellipse

Fly through the 3D Sierpinski pyramid:  
Fly Through the Sierpinski Pyramid Fr...

Drawing on a spinning white board:  
Amazing Spirograph

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