Fractals/Iterations in the complex plane/btm

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Boundary trace[1] [2]

BSM/J[edit | edit source]

BSM = Boundary Scanning Method

This algorithm is used when dynamical plane consist of two of more basins of attraction. For example for c=0.

It is not appropiate when interior of filled Julia set is empty, for example for c=i.

Description of algorithm :

  • for every pixel of dynamical plane do :
    • compute 4 corners ( vertices) of pixel ( where lt denotes left top, rb denotes right bottom, ... )
    • check to which basin corner belongs ( standard escape time and bailout test )
    • if corners do not belong to the same basin mark it as Julia set

Examples of code

  • program in Pascal[3]
  • via convolution with a kernel [4]

Dictionary[edit | edit source]

  • image
    • 2D
    • “segmented” image (an image with foreground pixels labeled 1 and background pixels labeled zero) = binary image
  • connectedness and neighberhood
    • 4
    • 8
  • boundary = boundary contour = contour
    • inner boundary (outermost pixels of foreground)
    • outer boundary (innermost pixels of background):
  • trace ( tracing)

papers[edit | edit source]

Video[edit | edit source]

Code[edit | edit source]

References[edit | edit source]

  1. wikipedia : boundary tracing
  2. Image Processing, Analysis, and Machine Vision Milan Sonka, Vaclav Hlavac, and Roger Boyle
  3. Pascal program fo BSM/J by Morris W. Firebaugh
  4. Boundary scanning and complex dynamics by Mark McClure