Escape-Iterations

Robert P. Munafo, 2008 Mar 17

"Escape-Iterations" is the name of a function often used to apply an easily-computable viewing representation to the Mandelbrot Set. It is a simgle-valued integer function that computes the iterates to using the simple algorithm shown below.

It is the easiest to compute, but perhaps the least informative: It serves adequately at showing the mu-atoms, but only hints at the presence of the filaments by providing contours that generally tend to be spaced more closely near the filaments.

function escape-iterations param("Z"): complex param("max_iterations"): integer result: integer begin function declare C : complex declare Z : complex declare iterations : integer declare still_iterating : boolean let still_iterating = true let iterations = 0 let C = Z while (still_iterating) do let Z = Z * Z + C let iterations = iterations + 1 if (magnitude(Z) > escape_limit) then let still_iterating = false else if (iterations >= max_iterations) then let still_iterating = false end if end while let result = iterations end function

The magnitude function computes the absolute value of the complex number Z.

There are other functions that can be used instead of escape iterations. The distance estimator function gives the best picture of what the Mandelbrot set "really" looks like.

See also DEM-dwell hybrid, binary decomposition, interior dwell.


From the Mandelbrot Set Glossary and Encyclopedia, by Robert Munafo.     Mu-ency index

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