String Art with Python

Veröffentlicht am: 16 Februar 2021
auf dem Kanal: Schattman Math

11,842

295

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:
   • Sound Waves in an Ellipse

Fly through the 3D Sierpinski pyramid:
   • Fly Thru a 3D Sierpinski Fractal

Drawing on a spinning white board:
   • Amazing Spirograph

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