The Buddhabrot fractal traces the orbits of the points outside the Mandelbrot set. What design considerations need to be taken into account to create a computerised sewing machine that traces out these orbits and produces the Buddhabrot fractal in a reasonable period of time (within a day) and still resemble a Buddhabrot?
2026-03-30 08:55:44.1774860944
Buddhabrot Sewing machine
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A Buddhabrot fractal,
is really just an artistic rendering of the standard Mandelbrot set
$$ z_{n+1} = z_n^2 + c $$
In the Mandelbrot set, you color points outside the set based off the number of iterations it takes to escape some predefined radius. In the Buddhabrot you still use the points outside the set, but you color the path of those points as they escape to infinity.
As such, the Buddhabrot is built up from many iterations of the mapping equation. Each pixel in the image is made up of many visits from many other starting pixels.
To make a sewing pattern you would need as way to build up an intensity by visiting it more than once, point by point. While I have little knowledge of sewing I'm not sure that this would be easy to do.