Target shaped fractals


Over the past few years I have done a lot of work in developing the science and technology of genetic fractals. At the very basis of it, they look like natural forms such as trees or other natural organisms.



Using the the artificial DNA language, I have managed to give shape and meaning to these fractals. My original idea was to approach engineering, i.e. the construction of useful objects from a genetic perspective: machines that grow themselves, just like plants.



This is still my idea, although many more ideas have been added to the list.

One of the things that both intrigue and bother me is that these fractal objects grown by the instructions of their DNA, is that they all do what nature does: they grow freely. The haphazard growth of tree branches, even if there is a high degree of symmetry, is still opportunistic. It grows where it wants.

This is intriguing because it shows the mechanics of nature from a simple (…) fractal mechanism. But it is also frustrating. As humans, we want to tame our world. When we design a sleak car, we don’t want bits of body work sticking out. We want to tame function and form. Yet, as a fractal designer, I want natural forms to evolve to meet our overarching design goals.

In the past few months I have turned into a new direction: taming the fractals. Although I had considered this before and experimented a little with it, I didn’t address it seriously until I saw the proposal for a 3D printed bridge in my home town Amsterdam.


[image credit: Joris Laarman Lab/Adriaan de Groot/MX3D]

I passionately love the idea but … the fractal structure in the design is made of straight lines! They should be smooth like my genetic fractals.

So I set to work and developed an algorithm to create arbitrary fractal tree structures that can fit into any shape – including the outline of a bridge. I call these “target shaped fractals”.

This was easier said than done because the concept is very different. A typical tree fractal grows where it wants based on its DNA.


But target shaped fractals start from a known point and all its branches have to grow to very specific points. Each branch has to be morphed to a specific shape that retains its smoothness all the way along its path. In a weird way, target shaped fractals are grown from the root AND the leaves.

Having worked all that out, I am pleased to report that I now have a mechanism to create these target shaped fractals. Right now the model is in 2D only and the next step is to enhance the model to 3D shapes.

At the top of this post is an image of a target shaped fractal that morphs to a circle. Below are two more of these target shaped fractals.

I now need to make one in a bridge shape and photo render it into an Amsterdam canal and send it to the guys at MX3D. I’m sure they’ll love it but whether they can use it is another matter. But I already have plenty of other ideas for these target shaped fractals and may look for other partnerships anyway.



11 thoughts on “Target shaped fractals

  1. Now that is a wild proposition… to grow a bridge. To grow a house, or temporary structure. I can see massive roll-on, roll-over, roll-off 3D printers.

    On another note, remember a while ago you said you might publish something (i’ve forgotten what, now) in a journal? Do you remember the name of the journal? I think it’s an online publication.


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