1. Drawing the Mandelbrot Set
Sep. 19
Dae-Eun Hyun
3D MAP Lab.

2. 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.

3. What is the Mandelbrot Set?
The points of the complex plane in two categories
Points inside the Mandelbrot Set
Points outside the Mandelbrot Set

4. 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

5. Computing the Mandelbrot Set
C inside the set
C outside the set

6. 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

7. Drawing the Mandelbrot Set
Color Intensity
Red
Blue
Num
Float v = d/ float Num;
glColor3f(v*v, v*v, v, 0.2);

8. 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

9. Drawing the Mandelbrot Set
Pseudocode for Drawing
for( j = 0; j < rows; j++)
for( i = 0; i < 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); }