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.

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.

The Gallery
Egypt: KMZ file

New capture in March 2019

South Korea: KMZ file

Malaysia: KMZ file

 Quotation: Jess Zimmerman ... If I hadn't looked them up, I'd suspect some of these were computer generated - but no, they're real rivers, lakes, and mountain ranges branching into mathematically and aesthetically beautiful patterns. [cut] Did you have any idea you lived inside a Mandelbrot set? Well, now you do.

Australia: KMZ file

Austria: KMZ file

 Quotation: Benoît Mandelbrot Why is geometry often described as 'cold' and 'dry'? One reason lies in its inability to describe the shape of a cloud, a mountain, a coastline, or a tree. Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line... Nature exhibits not simply a higher degree but an altogether different level of complexity.

Spain: KMZ file: courtesy Aurelio Garcia.

Spain: KMZ file courtesy of Eduardo Sáenz de Cabezón.

Spain: KMZ file courtesy of Juan Luis Varona.

Canada: KMZ file courtesy Richard Thomson.

Greenland: KMZ file

Saudi Arabia: KMZ file

 Quotation: Time Lightbox In a world made small and accessible by technology, it is easy to forget the magnitude of nature's infinite complexity. But sometimes technology reminds us, such as when trawling planet Earth on Google's Satellite View, zooming across landscapes partitioned by natural and unnatural boundaries.

Algeria: KMZ file

Features in the Diaorama Magazine, issue 4, May 2013.

United States of America: KMZ file

United States of America: KMZ file. courtesy of Emiel Boer.

Norway: KMZ file

 Quotation: Peter Aktins I wonder whether fractal images are not touching the very structure of our brains. Is there a clue in the infinitely regressing character of such images that illuminates our perception of art? Could it be that a fractal image is of such extraordinary richness, that it is bound to resonate with our neuronal circuits and stimulate the pleasure I infer we all feel?

Russia: KMZ file

China: KMZ file

Afghanistan: KMZ file

Burma: KMZ file

Features in the Diaorama Magazine, issue 4, May 2013.

 Quotation: Michael Barnsley Fractal geometry will make you see everything differently. There is a danger in reading further. You risk the loss of your childhood vision of clouds, forests, flowers, galaxies, leaves, feathers, rocks, mountains, torrents of water, carpet, bricks, and much else besides. Never again will your interpretation of these things be quite the same.

India: KMZ file

Laos: KMZ file

Mexico: KMZ file

South Africa: KMZ file

Namibia: KMZ file

Angola: KMZ file courtesy Pan Wolff.

Colombia: KMZ file courtesy Fernando de Paz.

Switzerland: KMZ file courtesy Lorant Buntye.

 Quotation: Pinar on "My Modern Met" The ridges and waterways in each aerial shot adds to the spectacular texture of each landscape. It's almost unbelievable that these naturally curving branches of paths exist in such extraordinarily beautiful patterns. The fact that it's a distanced view of the lands we walk on makes it that much more incredible and breathtaking. It really shouldn't come as such of a surprise, though, since it is a view of organically produced land. Many of the images bear a remarkable resemblance to textures and patterns found in a simple leaf, if one were to zoom in. Alternatively, we're looking at our vast world, zoomed out.

Venezuela: KMZ file courtesy Fernando de Paz.

Antarctica: KMZ file.

Tibet: KMZ file.

NearMap

There are mapping techniques that give higher resolution than Google Earth, namely aerial photography based upon surveys by planes or helicopters. Higher resolution in general would allow one to explore self similarity to smaller scales, that is, across a wider range of scales. The following examples are from an Australian product called NearMap, note that the sample areas tend to be on the coast and this is reflected in the examples presented.

 Click for high resolution image. KMZ file [Warning: 5700 pixel image]

 Click for high resolution image. KMZ file [Warning: 5400 pixel image]

 Click for high resolution image. KMZ file [Warning: 5700 pixel image]