## 1.12.2 Color scale bars

By default, plots with color maps with single-parameter color mappings are accompanied by color scale bars, which appear by default on the right-hand side of the plot. Such scale bars may be configured using the `set colorkey` command. Issuing the command

    set colorkey

by itself causes such a scale to be drawn on graphs in the default position, usually along the right-hand edge of the graphs. The converse action is achieved by:

    set nocolorkey

The command

    unset colorkey

causes Pyxplot to revert to its default behaviour, as specified in a configuration file, if present. A position for the key may optionally be specified after the `set colorkey` command, as in the example:

    set colorkey bottom

Recognised positions are `top`, `bottom`, `left` and `right`. `above` is an alias for `top`; `below` is an alias for `bottom` and `outside` is an alias for `right`.

The format of the ticks along such scale bars may be set using the `set c1format` command command, which is similar in syntax to the `set xformat` command (see Section 1.8.8), but which uses `c` as its dummy variable.

The positions of the ticks along color scale bars may be set using the `set c1tics` command command, which has similar syntax to the `set xtics` command.

An image of the Mandelbrot set.

The Mandelbrot set is a set of points in the complex plane whose boundary forms a fractal with a Hausdorff dimension of two. A point in the complex plane is defined to lie within the Mandelbrot set if the complex sequence of numbers

subject to the starting condition , remains bounded.

The map of this set of points has become a widely-used image of the power of chaos theory to produce complicated structure out of simple algorithms. To produce a more pleasing image, points in the complex plane are often colored differently, depending on how many iterations of the above series are required for to exceed 2. This is the point of no return, beyond which it can be shown that and that divergence is guaranteed. In numerical implementations of the above iteration, in the absence of any better way to prove that the iteration remains bounded for a certain value of , some maximum number of iterations is chosen, and the series is deemed to have remained bounded if . This is implemented in Pyxplot by the built-in mathematical function `fractal_mandelbrot(z,m)`, which returns an integer in the range .

`set numerics complex` `set sample grid 500x500` `set size square` `set nokey` `set nocolkey` `set log c1` `plot [-2:2][-2:2] fractals.mandelbrot(x+i*y,70)+1 with colormap`