Fractals/Iterations in the complex plane/btm

Boundary trace

BSM/J

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 $z$ do :
  • compute 4 corners ( vertices) of pixel $z_{lt},z_{rt},z_{rb},z_{lb}$ ( 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
• via convolution with a kernel

Dictionary

• 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)
  • Contour Tracing Algorithms by Abeer George Ghuneim

papers

• Boundary tracing in binary images
• Wilhelm Burger · Mark J. Burge: Digital Image Processing An algorithmic introduction using Java

Video

• Mandelbrot Animation (Boundary Tracing / Recursion) by Gnarly Charley

Code

• fractint
• Java code ( from the video) by Gnarly Charley ( charlesk26 )
• Tracing Boundary in 2D Image Using Moore Neighborhood Approach in C++ by Udaya K Unnikrishnan
• Moore Neighbor Contour Tracing Algorithm in C++ BY ERIK SMISTAD
• Potrace(TM) is a tool for tracing a bitmap by Peter Selinger