The above image is cropped and scaled from a larger image. Click the image above to obtain the full version (approx. 11.7 MB).
In the morning, I often have a cup of coffee. I will generally add some cream or half-and-half to my hot beverage, both for the flavor and to cool things down to a drinkable level. As the cream mixes with the coffee, it swirls and billows, creating abstract patterns. The dynamics of the fluids are seemingly captured in the whirls and eddies of many regions of the Mandelbrot set.
This particular region of the Mandelbrot set is near \(-0.5+0.5i\). The image above is about one ten thousandth of a unit across, while the larger image is about one thousandth of a unit across (give or take a bit). This region sits on the edge of the Mandelbrot set to the ‘north’ (positive imaginary component) of Seahorse Valley. The region contains seahorse-like structures, but they are less clearly defined.
It is also interesting to note the miniature Mandelbrots in both images. Many of them seem to be skewed and off-center. They repeat the general theme of the Mandelbrot set as a whole, but are not identical. Fractals are defined by self-similarity at all scales, but this similarity need not consist of identical copies—like music, fractals contain variations on a theme.