48.3 Definitions for complex fractals

Function: mandelbrot_set (x, y) ¶

Mandelbrot set.

Example:

This program is time consuming because it must make a lot of operations; the computing time is also related with the number of grid points.

(%i1) load("fractals")$
(%i2) plot3d (mandelbrot_set, [x, -2.5, 1], [y, -1.5, 1.5],
                [gnuplot_preamble, "set view map"],
                [gnuplot_pm3d, true],
                [grid, 150, 150])$

Function: julia_set (x, y) ¶

Julia sets.

This program is time consuming because it must make a lot of operations; the computing time is also related with the number of grid points.

Example:

(%i1) load("fractals")$
(%i2) plot3d (julia_set, [x, -2, 1], [y, -1.5, 1.5],
                [gnuplot_preamble, "set view map"],
                [gnuplot_pm3d, true],
                [grid, 150, 150])$

See also julia_parameter.

Option variable: julia_parameter ¶

Default value: %i

Complex parameter for Julia fractals. Its default value is %i; we suggest the values -.745+%i*.113002, -.39054-%i*.58679, -.15652+%i*1.03225, -.194+%i*.6557 and .011031-%i*.67037.

Function: julia_sin (x, y) ¶

While function julia_set implements the transformation julia_parameter+z^2, function julia_sin implements julia_parameter*sin(z). See source code for more details.

This program runs slowly because it calculates a lot of sines.

Example:

This program is time consuming because it must make a lot of operations; the computing time is also related with the number of grid points.

(%i1) load("fractals")$
(%i2) julia_parameter:1+.1*%i$
(%i3) plot3d (julia_sin, [x, -2, 2], [y, -3, 3], 
                [gnuplot_preamble, "set view map"],
                [gnuplot_pm3d, true],
                [grid, 150, 150])$

See also julia_parameter.