Drawing the Mandelbrot Set

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Drawing the Mandelbrot Set

• Sep. 19
• Dae-Eun Hyun
• 3D MAP Lab.

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What is the Mandelbrot Set?

• Def. The Mandelbrot Set M is the set of all
  complex numbers c that produces a finite orbit of
  0.

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What is the Mandelbrot Set?

• The points of the complex plane in two categories
• Points inside the Mandelbrot Set
• Points outside the Mandelbrot Set

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Computing the Mandelbrot Set

• How we can decide the convergency?
• Set the maximum magnitude of Zk
• Typically 2
• How many we have to iterate?
• Set some upper limit Number on the maximum
  number of iterations
• Typically 100 400

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Computing the Mandelbrot Set
C inside the set
C outside the set
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Drawing the Mandelbrot Set

• Display M on the raster graphics
• Set up a correpondence between each pixel on
  the display and a value of C, and the iteration
  number for that C-value is found.
• Example
• Bright yellow to C near outside the set
• Dimmer yellow to C farther away from the set
• Deep Blue to C have the small iteration Num

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Drawing the Mandelbrot Set
Color Intensity
Red
Blue
Num
Float v d/ float Num glColor3f(vv, vv, v,
0.2)
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Drawing the Mandelbrot Set

• How to associate a pixel with a specific complex
  value of C
• Image the Number of Rows
• the Number of Columns

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Drawing the Mandelbrot Set

• Pseudocode for Drawing
• for( j 0 j lt rows j)
• for( i 0 i lt cols I)
• find the correspondence c-value for Pixel
  (i,j)
• estimate the iteration Number of the
  orbit
• find Color determined the iteration
  Number
• setPixel(j, i, Color)