# Fractals/Iterations in the complex plane/btm

Boundary trace[1] [2]

## 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 ${\displaystyle z}$ do :
• compute 4 corners ( vertices) of pixel ${\displaystyle z_{lt},z_{rt},z_{rb},z_{lb}}$ ( 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[3]
• via convolution with a kernel [4]

# 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)