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Dan Wills Fractal Explorer and Digital Image Synthesist Science to Sage Magazine would like to acknowledge Dan Wills and his amazing fractal Art. His work has graced many of our issues enhancing and enlivening the written words of innovators and world thinkers - thank you Dan.

Dan始s Work, Authors Words, Karen始s Design

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Dan Wills

Fractal Explorer and Digital Image Synthesist

Are images of fractals art?

It's up to each individual

to decide what they believe about that. I would suggest that they are only partially artistic. Some might say that a photo of a tree was artistic, however the beauty in it has come from a natural process. The photographer has used a combination of luck and skill in order to get the image, the same is true of fractals. Unless you're inventing new formulas yourself, it's most fair to liken the process of generating fractal imagery to a kind of mathematical photography. The subjects of the work are the formulas, and it's difficult to add any deeper message to a fractal work. Certainly there is lots that you can control in terms of how the landscape is dressed and presented, but most of the lay of the land is already defined by inescapable mathematical (or, more generally: computational) fact. I personally believe that the universe is here because of selforganization (or self-synthesis, you could say). Fractals are tied to self-organization, as the automatic processes of self-organization help to build linkage across scale levels that gives rise to selfsimilarity. If we look into the natural world we see that self-organizing systems often do generate fractals. Perhaps this scale-invariance is caused by the action of a central 'story' - like a proto-self, that governs self-generation spanning many scale levels. Perhaps we love looking at fractals because we feel related to them? They resemble things within us and surrounding us - and they abstractly illustrate the primal story of imaginary things becoming real. Dan Wills

I have been generating digital fractal images for many years

- going back to a glorious day on which I un-deleted an archive of

Fractint (an old DOS fractal program) from a floppy disk. For some years now I have used a Windows application called UltraFractal. I run it under the Linux operating system (using an emulation software called 'Wine'). UltraFractal is essentially a 'photoshop'-like layering and compositing software for fractals. Fractals are defined and colored by iterated transformations of complex numbers - in short - by formulas. UltraFractal has a large, diverse and actively developed formula collection. I've done a very small amount of formula authoring, not enough to say that I've really mastered it, besides my math is not strong enough to really do it properly. I tend to focus my programming abilities elsewhere, I've written (in python) and released a little software tool called 'uprMash' that manipulates UltraFractal UPR files (saved fractals). The idea behind uprMash is to explore motion-blur in fractals: The concept that the virtual 'shutter' could be left open while one of the fractal parameters is varied, leading to a range of states being blended together. It was quite refreshing to see fractals which didn't have everything perfectly in focus, some nice results from uprMash can be seen on my Picasa galleries (

The activity of the formula authors and the wider UltraFractal community is one of my inspirations. Many excellent insights and fascinating new ideas, suggestions and pointers from fellow fractal explorers have led me to delve into these beautiful, bizarre, intensely abstract fractal places. I share credit with the community for bringing these images into reality for all to see. Another thing that spurs me on in creating these images is the satiation of a peculiar curiosity about the finer structures in an existing fractal image. Zooming in, resolving more detail, the desire to find out what something looks like closer up. Looking towards a literally-infinite micro-scale horizon. The use of fractal software in discovery, manipulation and focusing to resolve certain features or textures in fractals is a thrill that is mostly reserved for the person using the fractal software (who you would normally call the 'artist'). I agree with the Orbit-Trap bloggers about this at least: A major part of the 'art-experience' that happens to-do-with fractals, is the actual experience of exploring. The operator of the software IS the audience, at least in part. The desire to share the beauty of the exploration experience for this universe of image synthesis is something that encourages me to take these photos along the way. To let others see what I saw on the journey. I also explore fractals to discover unique aesthetic qualities. There is occasionally the exciting possibility that one might be the first human to have discovered some of these places. Indeed there is infinite variability in the shapes and textures in the vast universe of computationally definable images. The kinds of infinity you're dealing with are way beyond astronomical, and this is mind-boggling in a very pleasant way.

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Dan Will and Fractal Art  

Fractal Explorer and Digital Image Synthesist Science to Sage Magazine would like to acknowledge Dan Wills and his amazing fractal Art. His...

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