Posts Tagged ‘Paul Nylander’

Meshing Gears

January 12, 2014

Another fabulous image by Paul Nylander at bugman123.com.

image by Paul Nylander bugman123.com

A set of 242 interlocking bevel gears arranged to rotate freely along the surface of a sphere. This sphere is composed of 12 blue gears with 25 teeth each, 30 yellow gears with 30 teeth each, 60 orange gears with 14 teeth each, and 140 small red gears with 12 teeth each. I also found 3 other gear tooth ratios that will work, but this one was my favorite because the small gears emphasize the shape of a truncated rhombic triacontahedron.

From Mandelbrot to Mandelbulbs with Chaos in between

October 31, 2013

The Mandelbulb is a three-dimensional analogue of the Mandelbrot set, constructed by Daniel White and Paul Nylander using spherical coordinates. A canonical 3-dimensional Mandelbrot set does not exist, since there is no 3-dimensional analogue of the 2-dimensional space of complex numbers. It is possible to construct Mandelbrot sets in 4 dimensions using quaternions. However, this set does not exhibit detail at all scales like the 2D Mandelbrot set does.

From bugman123

an 8th order Mandelbulb set by bugman123

Here is my first rendering of an 8th order Mandelbulb set, based on the following generalized variation of Daniel White’s original squarring formula:
{x,y,z}n = rn{cos(θ)cos(φ),sin(θ)cos(φ),-sin(φ)}

Paul Nylander, bugman123.com

A classic Mandelbrot set

Mandelbrot set – Wikipedia


%d bloggers like this: