The Weird Inner World of the 3D Fractal

This post is about one of the really cool things that happens when maths I don’t understand and technologies I don’t understand get together to make something awesome. Let us begin:

A typical fractal, made using the Mandelbrot set.


A fractal is a conceptual object that reveals further details about its shape ad infinitum, upon ever-closer inspection of it’s fabric. Think of the trunk of a tree sprouting branches, which in turn split off into smaller branches, which themselves yield twigs etc and you won’t go far wrong. In fact, fractals typically look like this thing to the right.

These infinitely complex shapes are ‘created’ by instructing graphics software to render the result of a simple mathematics formula. Until now, the result has been a 2D image – there’s no depth, shadow, perspective, or light sourcing. It is a truly abstract mathematical shape.

But since your home computer became powerful enough to do proper image rendering stuff, home hobbyists have begun to innovate on these formulae. For the first time, three dimensional fractals are able to be created with relative ease.

I can’t go into the maths, because you know, I’m not a total geek, but I do want to show you how beautiful some of these shapes are. Let’s run through some examples:


This is what you get by multiplying phi and theta by two.


More like a classic fractal with 0.5*pi to theta and 1*pi to phi.


This time multiplying angle phi by two, but not theta.




But we’re still looking at these things from outside. The really cool bit is when you start to zoom in. So let’s look at some of the high quality renders from the archives of Daniel White at his highly eclectic Skytopia, where I first learned of this phenomenon.

Make sure you click around on some of these thumbnails, yeah?!

If you’re anything like me, you’d be pretty excited at the idea of being able to create both beauty and complexity from something as simple as a few lines of code, and to then be able to explore your creation from every angle.

Then again, if you’re anything like me, you’d feel a bit frustrated that you’ll probably never be able to make something that awesome yourself. So let’s marvel at the wonder of Daniel’s creation as he takes us deep ‘Into the Heart of the Mandelbulb’.

Your comments, please!

Into the Heart of the Mandelbulb

Conclusion

I set out to assess the implications of a wholly new medium, one which had received little academic attention written from a media theoretical perspective. I made clear use of an industry connection to gain inside knowledge of the developments occurring to bring this medium to the mainstream. Building a methodology that could sustain the level of analysis that I hoped to achieve, I observed the interactions between technology and industry, market forces and cultural influences. Having positioned my subject at the crest of a curling wave, I employed critical media theory to explore the potential implications of my subject in its wider context of social reality. This ambitious task has granted me insight into how the complex interactions of various fields give rise to social change. Along the way I have revealed seams rich in potential for further analysis.

McLuhan is proven to apply to yet another medium, the perspective he offers served my analysis quite well. A further exploration might make use of his Acoustic and Visual Space probe, Cavell’s basis for McLuhanistic spatial enquiry in his book McLuhan in Space (2002) would be a good starting point for such work, since it applies McLuhanism to the media of time and space, thus a good start for work on the presence of virtual objects. Media analysts occupied with screen design might wish to extend Bolter and Grusin’s (1999) work on remediation to the emergent Mobile AR technology, perhaps from an explicit digital gaming perspective. Those with interest in advertising or business as applied to Augmented Reality would do well to continue Benjaminian thought to its logical end: manipulating a virtual object to hold added-value for commercial enterprise. Those with a more creative bent might enjoy a study of the public perception of AR artworks using Benjamin also. There is scope for research into AR-based social interactions; gaming styles; immersion and identity formation, but this sort of work necessitates that first Mobile AR spends at least some time in public consciousness.

Finally, I believe that I have convincingly laid out an argument showing that AR is currently being developed and packaged as an entertainment technology, but its potential for community-driven, self-proliferating excitement of user-created content makes AR a significant and culturally-transformative technology. Convergence between media types will enable and drive the creation of innovative content which if successful will itself rely on new ways of accessing and viewing content and ultimately new forms of content and user experience entirely. We are at the crest of a wave. Will it wither and let a larger wave pass above it, or will it grow to reach tidal proportions? Despite my predictions, only time will tell.

Web Discoveries for May 27th

These are my del.icio.us links for May 27th