Google Earth fractals Written by Paul Bourke

Started: October 2010. Last updated: October 2012 Most of the images here can be supplied in higher resolution for printing, for a small fee. Introduction The following is a "photographic" gallery of fractal patterns found while exploring the planet with Google Earth. Each is provided with a KMZ file so the reader can explore the region for themselves. Readers are encouraged to submit their own discoveries for inclusion, credits will be included. Besides being examples of self similar fractals, they are often very beautiful structures ... not an uncommon characteristic of fractal geometry. Index Egypt South Korea Malaysia Australia Austria Spain Canada Greenland Saudi Arabia Algeria USA Norway Alaska Russia China Afghanistan Burma India Laos Mexico South Africa Namibia Angola Colombia Venezuela Switzerland Antarctica Tibet Self Similarity Fractals are usually associated with self similarity across scales. For pure/idealised mathematical fractals the self similarity may be across an infinite range of scales, such as the Sierpinski Gasket. In real life and in nature the self similarity is only across a range of scales. Branching structures, such as most of the examples shown here, are classic examples of self similarity across 2, 3 or 4 scales. As with many plants, a thick branch (trunk) branches into one or more smaller branches, which in turn split into one or more smaller branches, and so on. The structure is similar at each scale, from the twigs to the main tree trunk. An example of this for a river system is illustrated below [KMZ file], clicking on an image will give the high resolution version of the image without the markings. For the image on the right the pixel size is 30cm, the image on the right has a pixel size of 7.5cm. At each scale the branching structures are similar in appearance. [Warning: the full size images are large.] Another way to think about whether something exhibits self similarity is if it can be interpreted to exist at different scales. Consider the two images below, they can be imagined to be perhaps a stone of a few centimeters wide, a meter wide if imagined to be a rock face, or in the case of a mountain they may be a few kilometers wide.

