Quadratic Julia sets.
|Download juliaset console program (Windows 64bit)||Download juliaset source code (Lazarus/Free Pascal)|
Description: Very simple program to draw quadratic Julia sets. Scaling and zooming are set
by entering the values using the keyboard and are rather elementary. Please have a look at the "juliaset readme" file,
included in the .zip archive, for details.
Beside its definition in the context of complex dynamics, a topic of mathematics, Julia sets may be defined as follows: If f is an entire function, then J(f) is the boundary of the set of points which converge to infinity under iteration; if f is a polynomial, then J(f) is the boundary of the filled Julia set; that is, those points whose orbits under iterations of f remain bounded.
Quadratic Julia sets are generated by considering the functions fc(z) = z^2 + c, where c is a complex constant. For various values of c, various Julia sets (with various shapes) are obtained. Using different colors for different numbers of iterations produces an infinity of vary different colorful pictures.
Improvement: Implement scrolling using cursor keys instead of keyboard entry of scaling values.
Free Pascal features: Console drawing of mathematical functions using the graph unit.
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