Rich Wareham
'The surface of a hyper-complex escape-time fractal'
Engineers often exploit a mathematical 'trick' for combining two regular numbers into one 'complex' number allowing them to carry twice the information around inside their equations. The behaviour of these complex numbers can be... well... complex. Their ability to produce strikingly detailed images from very simple equations is one observation of the so-called 'Chaos Theory'. In this image we have extended complex number to hold more than just two regular numbers. In this case we are storing four. These 'hyper-complex' numbers can be used to generate fractals just like their regular two-numbered brethren. This image is a visualisation of a three dimensional 'slice' through the four-dimensional surface of one of these hyper-complex fractals generated in real-time via ray-tracing on a consumer-grade graphics card.
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