C3Subtitles: 31c3: Higher-Dimensional Geometry and Fractals
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Higher-Dimensional Geometry and Fractals

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Video duration
00:30:51
Language
English
Abstract
Extending the common 3-space-to-2-space projections to 4D and higher and how certain types of fractals can be presented using these expansions. After that we'll have a closer look at Fractal Flames as used in Electric Sheep.

This talk will be split into 3 parts; first: extending the common 3D-to-2D projections - used by libraries such as OpenGL - to also allow projecting hypothetical 4D or higher constructs to a 2D screen.

Second: making pretty fractal pictures by rendering iterated function systems with affine transformations in 4D and higher. This part explains how the chaos game works and how to do an alternate, discrete render which works better in higher dimensions than 2D.

The third and final part takes a look at the Fractal Flames by Scott Draves, a different kind of iterated function system used in the Electric Sheep screen saver. The original algorithm for this is inherently 2D, but parts of it can be extended to higher dimensions, producing interesting results.

Due to time constraints, it is assumed that the audience is already roughly familiar with - or willing to believe in - the general method for 3D projections, including vector and matrix maths. There will also be pretty pictures.

The presentation will have live demo segments mixed in, which make use of a F/OSS 4D+ primitive and fractal renderer called "Topologic" (see links, below).

Talk ID
6072
Event:
31c3
Day
3
Room
Saal G
Start
11:30 p.m.
Duration
00:30:00
Track
Science
Type of
lecture
Speaker
Magnus