88 AUGUST 2007 | LINUX FOR YOU | www.
linuxforu.
com
C M Y K
IIIII
n most of the cases, writing fractal programs requires a
good knowledge of mathematics.
The Mandelbrot set is
based on the theory and use of complex numbers.
The
Mandelbrot set is a...
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88 AUGUST 2007 | LINUX FOR YOU | www.
linuxforu.
com
C M Y K
IIIII
n most of the cases, writing fractal programs requires a
good knowledge of mathematics.
The Mandelbrot set is
based on the theory and use of complex numbers.
The
Mandelbrot set is a collection of complex numbers, which
have two parts: real and imaginary.
Usually, a complex
number is represented in the form, a + bi , where a is the
real part and b is the imaginary part (the suffix i
indicates that).
A complex plane has real numbers in the xaxis and imaginary numbers in the y-axis.
Given the complex numbers Z and C, the Mandelbrot
set is formed by the formula: Z = Z ** 2 + C.
Here ** stands
for square.
C is the number we test to see if the number is
inside or outside the set.
We start Z from zero and keep
reassigning it as we change C, using this formula.
Given a complex number a + bi, the formula for finding
the square of a complex number is: a**2 – b**2 + 2abi.
So,
the real part is a**2 – b**2 and the i
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