minow@decvax.UUCP (Martin Minow) (08/07/85)
I recently posted a pair of programs to compute and display
the Mandelbrot set (as described in Scientific American, Aug.
1985) to net.sources. In the readme.txt that accompanied the
posting, I suggested that this software would make an interesting
project for an introduction to computing sciences course. This
note expands on that comment, suggesting a few "homework assignments".
It presupposes familiarity with the article.
1. (easy) Although the program deals with complex numbers, it does
not define a complex datatype such as
typedef struct complex {
double real, imag;
} COMPLEX;
but rather defines the variables as, for example, z_real and z_imag.
Why? What does this tell you about the C language, compilation
techniques, and the adaptation of programming style to real-world
problems?
2. (harder) The program uses double-precision floating point variables
to compute each set. However, we know that the range of the (interesting)
values is real [-2.0,+.50] and imag [-1.25,+1.25].
Can the program be redesigned to use scaled fixed-point arithmetic?
Would it be faster without losing accuracy?
Can the computations be carried out in polar coordinates in a sensible
manner?
3. (hardest) The program computes each point independently of all others.
I.e, the algorithm may be summarized as follows:
for (i = 0; i < npixels; i++) {
for (j = 0; j < npixels; j++) {
compute set at pixel[i][j];
}
}
Can the value at pixel[i][j] be used to compute the value at
pixel[i][j+1] or are the values truely independent? Looking
at the displayed results suggests a correlation.
Have fun.
Martin Minow
decvax!minow