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To make a density map from a 2D set of data, the first step is to compute values for the third dimension. (Gnuplot has no facilities for computing these values automatically.) The simplest way is to make a 2D histogram; the plot is divided in small 2D regions, and the z-values are proportional to the number of points inside these regions. The following Python script will make an histogram from a time series of two dihedral angles.

The original Mandelbrot is an amazing object that has captured the public's imagination for 30 years with its cascading patterns and hypnotically colourful detail. It's known as a 'fractal' - a type of shape that yields (sometimes elaborate) detail forever, no matter how far you 'zoom' into it (think of the trunk of a tree sprouting branches, which in turn split off into smaller branches, which themselves yield twigs etc.). It's found by following a relatively simple math formula. But in the end, it's still only 2D and flat - there's no depth, shadows, perspective, or light sourcing. What we have featured in this article is a potential 3D version of the same fractal.