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.
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, 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.
Wildfire is a free and user-friendly image-processing software, mostly known for its sophisticated flame-fractal-generator. It is Java-based, open-source and runs on any major computer-plattform. There is also a special Android-version for mobile devices.
Fractorium and its associated command line tools can render fractal flames using the CPU, or OpenCL. In order to use OpenCL, you must have an nVidia card that has the Fermi architecture or later, or a recent AMD card. If you attempt to use an unsupported card, you will receive an error message and the CPU renderer will be used instead.
Chaotica is a next-generation fractal art application, designed for both novices and professional artists.
Novice users can enjoy editing randomised fractals to produce stunning HD wallpapers and animations.
Professional users will particularly value the fast, modern rendering engine. High quality animations and huge images for print are easily produced, with real-time imaging controls that will dramatically accelerate your workflow.
What is fractal art?
Fractal art is a digital art medium with a very rich creative space, based on geometry and recursion.
Chaotica's user interface abstracts much of the maths away to provide a fluid artistic process.
Since its invention in 1981, IFS fractals have been popularised by Flam3 and Apophysis. Chaotica extends the creative possibilities of these programs in a powerful, production-oriented environment.
Some example here : https://www.tfmstyle.com/fractality-project