Buddhabrot Sewing machine [closed]

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?

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closed as off topic by Grumpy Parsnip, vonbrand, Jim, Alex Becker, SashaApr 15 '13 at 5:11

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it would not be mathematically accurate.... but why not? this is not really a mathematical question, is it? take a picture of the buddhabrot and sew every pixel on its own if you have to. theoretically that is possible.... –  example Jan 17 '13 at 1:03
This does not appear to be a mathematical question, and actually I have no idea what the question means. –  Grumpy Parsnip Jan 17 '13 at 1:59
It was an interesting question and I didn't know where else to go. I don't mind if its moved to a different stack exchange site but I didn't see any fractal dimension sewing pages. This wouldn't be every pixel, the orbits go from point to point on the screen and the sewing machine would move the thread from each point following the orbit. –  Jordan Brown Jan 17 '13 at 2:04
Okay, but then how does your question differ from asking whether it's possible to make a machine which can move a needle to a given point? Isn't that obviously possible? –  Grumpy Parsnip Jan 17 '13 at 12:12
but would it forever to finish the work of art –  Jordan Brown Jan 17 '13 at 21:38

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.

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