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Recently I discovered how to combine different fractals into one image. This is a very exciting development that opens up whole new realms of possibilities for my artwork. Currently I am able to combine fractals that I have created within the fractal program Apophysis.

What is a Fractal in a Fractal?

The inner workings of Apophysis will be addressed in a future article. Suffice to say, I am controlling the way the internal chaos rendering engine that Apophysis uses to make the final image. Instead of all the points being plotted everywhere on the screen, I am giving them a destination to travel towards, and therefore taking more control over the rendering process. The result is that I can create one fractal, and then “insert” it into an entirely different fractal, all within the same fractal. In words (and even in practice) it can be confusing, so let’s look at a graphical representation.


Above you can see that I’ve used to distinct fractal styles (two bottom images) and combined them into one fractal (top image). The actual images on the bottom do not appear in the top fractal image but are used only to illustrate the style of fractal being used in each. In the above situation the first image on the bottom is known as a gnarl, and the gnarl is placed inside the second fractal style, known as plastic or plastic bubbles. The result of combining the two is shown in the top image.

Can this idea be expanded upon?

Yes! Theoretically one could continue to put fractals inside fractals inside fractals etc. I have successfully created a three in one fractal as outlined below.

The difficulty with this process is two-fold. First there’s the an issue of it becoming increasingly confusing to work with the fractal the more complex it gets. The second problem is that of quality. With each encapsulation of a fractal the quality of the image diminishes. I’m working hard to alleviate this problem, however it could be something inherit to IFS fractals in general. Not something I can tackle at the moment.

Where do you intend on going from here?

I have many ideas to take advantage of the above technique as well as to expand upon it. Unfortunately I do not intend to reveal those ideas here! You’ll have to wait and see what new discoveries will come about. Below are a few more examples of pieces that I’ve completed where two or more fractals have been combined.