MandelbrotSetDistance
MandelbrotSetDistance[c]
estimates the distance from c to the nearest point in the Mandelbrot set.
MandelbrotSetDistance[c,"Interior"]
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.
Examples
open allclose allBasic Examples (2)
Scope (2)
Options (2)
MaxIterations (1)
Sometimes MaxIterations needs to be increased to get a nonzero distance:
WorkingPrecision (1)
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:
Text
Wolfram Research (2014), MandelbrotSetDistance, Wolfram Language function, https://reference.wolfram.com/language/ref/MandelbrotSetDistance.html.
CMS
Wolfram Language. 2014. "MandelbrotSetDistance." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/MandelbrotSetDistance.html.
APA
Wolfram Language. (2014). MandelbrotSetDistance. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/MandelbrotSetDistance.html