(maxima.info)Definitions for complex fractals

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60.3 Definitions for complex fractals
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 -- 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'.

 -- 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'.

 -- 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'.