estimates the distance from c to the nearest point in the Mandelbrot set.
estimates the distance from c to the nearest point in the complement of the Mandelbrot set.
Details and Options
- The Mandelbrot set is the set of all complex numbers c for which the sequence does not diverge to infinity when starting with .
- With the option MaxIterations->n, the sequence will be iterated at most n times to determine the distance. The default setting is MaxIterations->100.
- As MaxIterations approaches infinity, MandelbrotSetDistance[c] will converge on a number that is guaranteed to be at least the true distance.
Examplesopen allclose all
Basic Examples (2)
Estimate the distance from to the Mandelbrot set:
MandelbrotSetDistance is useful for making stark binary images of the Mandelbrot set:
Sometimes MaxIterations needs to be increased to get a nonzero distance:
Increase WorkingPrecision to get a more precise answer:
Properties & Relations (1)
Neat Examples (4)
Combine interior and exterior distance information:
Display the distance to the Mandelbrot set from points on one-quarter of the unit circle:
Represent the distance to the complement of the Mandelbrot set as height:
Display distance to the Mandelbrot set as height:
Display the distance from the exterior of the Mandelbrot set using color:
Wolfram Research (2014), MandelbrotSetDistance, Wolfram Language function, https://reference.wolfram.com/language/ref/MandelbrotSetDistance.html.
Wolfram Language. 2014. "MandelbrotSetDistance." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/MandelbrotSetDistance.html.
Wolfram Language. (2014). MandelbrotSetDistance. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/MandelbrotSetDistance.html