Mandelbr displays the Mandelbrot set.

The Mandelbrot set is a set of points in the complex plane. In the complex plane the real part of a complex number is represented along the x-axis, and the imaginary part along the y-axis. A point z[0] in the complex plane is member of the Mandelbrot set, if the sequence z[n+1] := z[n] ** 2 + z[0] (for n >= 0) is bounded. That is, a complex number, z[0], is in the Mandelbrot set if, when applying the iteration repeatedly, the absolute value of z[n] never exceeds 2. If the absolute value of any z[n] becomes larger than 2, the sequence will escape to infinity. The boundary of the Mandelbrot set forms a fractal.

The points of the Mandelbrot set are displayed in black. For unbounded points the number of the iteration n, for which abs(z[n]) >= 2.0 holds, is mapped to a color. For practical purposes the program limits the iterations to a maximum of 256 and assumes that a point is member of the Mandelbrot set if reaching this limit.

The program accepts the following mouse commands:

• The left mouse key selects a new center and magnifies by factor 2.
• The middle mouse key selects a new center.
• The right mouse key scales down by factor 2.