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Playing with fractals

Producing images that are self-similar in different scales

March 26, 2013

Although it is common to hear of fractals, Robert Fathauer introduces us to the theme in a very particular way: he invites us build a fractal representation with natural elements, more specifically trees.

Although the concept of fractal in nature differs slightly from the concept of mathematical fractal (because in nature self similarity is not taken to infinite levels of detail), the idea is to produce images that are self-similar in different scales, this is, that regardless of the “zoom” we do to the image, we always see the same.

What Robert Fathauer proposes is to choose a tree branch to be the model for our object and begin by taking a photo of it. We can then compose one or more photos to create the building block of our tree (block A – the first generation).

Block A

Then we make a copy of the building block and adjust the size of it so that the wider end of the new block has the same width as the upper end of block A.

(Note: the adjustment must be the same vertically and horizontally under the same reason, it is not supposed to “stretch” the image).

A new branch is represented above the first construction block, block A.

We repeat this process until the diameter of our building block is too small, not forgetting to do the same procedure for the branches that emerge in the tree.

New branches are to be built in each point represented in red.

After some iterations, the end result will be an original tree:


However, not all trees built using this process have such a “natural” aspect as in this case.

This may be due to the angle of inclination of the branches that constitute our building block A or the curvature they may have.

More relevant than their beauty, is the functionality of fractals due to their characteristics.

They allow the analysis of phenomena or data in various fiels: in medicine, for example, they are used in quantitative diagnostic procedures of pathologies such as cancer; in biology they are used to measure the roughness of fungi and in industry they are useful in the automatic detection of product faults.

They are even necessary in economy, in the analysis of financial fluctuations.

But none better than Benoit Mandelbrot, pioneer at the work of fractal geometry , to talk about fractals. Here is his TEDtalk:


Based on the article Fathauer, Robert W (2011), Photographic Fractal Trees, Bridges 2011 Proceedings,available here.  (Accessed on the 24th of March 2013).

Written by Susana Pereira

Susana Simões Pereira, maths teacher and PhD in science teaching and communication. I enjoy games and photography and I'm passionate for science and art, specially when together in the same context. You can follow my updates on Twitter, LinkedIn and Facebook.