### 60.3 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])$

  Categories:Package fractals ·

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`.

  Categories:Package fractals ·

Optional 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`.

  Categories:Package fractals ·

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`.

  Categories:Package fractals ·