The Sunflower Plot
Scatter plots become difficult to read when the density of plot points becomes high because of the overlapping plot symbols. William Cleveland and R. McGill introduced the sunflower plot as a solution to this problem in 1984. The original concept had certain disadvantages and, despite some improvements in the sunflower plot design during the next twenty years, software for drawing sunflower plots never became generally available.
In 2003 William D. Dupont and W. Dale Plummer, Jr. of the Department of Biostatistics at Vanderbilt University School of Medicine published a paper describing an improved sunflower plot design (Journal of Statistical Software 2003; 8 (3)) and provided a documented Stata program called sunflower, for drawing the graphs. This paper was the inspiration and knowledge-base for implementing the sunflower plot facility for the second release of Antaeus on May 1, 2009.
In Antaeus up to 5 degrees of sunflowers are used as necessary, with increasing numbers of observations per petal, and with each degree using different colors. For data cubes containing less than 20,000 records (observations), sunflower plots are of limited or no use. Regular scatter plots would be likely to show more information. Now consider the following sunflower plot from the Star Data demo cube that contains about 120,000 records:
The Hertzsprung-Russell Diagram shown here is much used in astronomy. Using a regular scatter plot with this many data points would result in a solid black mass in the central area of the plot. The variation in density within the mass would be invisible. In the sunflower plot the variation in density is not only visible because of the data content of the "flowers", but also because of the effect of flowers with a higher number of petals literally looking denser than those with fewer petals—the graphical equivalent of onomatopoeia in language.
Antaeus also gives you the option of using a "pixel" scatter plot, where each plot symbol is a single pixel. With this type of scatter plot, the variation in density shows up quite well using the above data and lessens the need of a sunflower plot in this case. But consider the following pixel scatter plot that uses data from a cube with about 2.5 million records:
This pixel scatter plot is mostly a solid black mass and does not show variation in density within the mass (unless you use magnification). Now look at a sunflower plot of the same data:
A sunflower plot will draw very much faster than its equivalent regular scatter plot when the number of observations is great. This is because accumulating the counts of observations falling into the hexagon bins where the flowers are drawn is pure number-crunching, which is done at blinding speed by your super-computer. Drawing 2,500 sunflowers takes much less time than drawing 120,000 small circles. Note that the same number of 2,500 sunflowers would be used for drawing a sunflower plot of one million or ten million observations. This makes it practical to draw sunflower plots for very large numbers of observations, as was done above.