a perspective on mathematics, the pattern, and the abstract

Posts tagged: 3D

Specular holograms by Matthew Brand currently on display at the new Museum of Mathematics in New York.

See his site for more.

The technique used by Brand to create these pieces is not one of conventional holography. He meticulously controls the unique shape of thousands of tiny optical pieces placed on a surface creating a 3D effect when the light source or viewer moves. This is essentially a mathematical problem in differential geometry and combinatorial optimization. Brand was the first person to correctly describe this technique in 2008 even though it dates back as early as the 1930s (check out his paper for details).

This is what it would look like to spin around in 3 dimensional hyperbolic space tiled by regular right angled dodecahedron.

Created with Curved Spaces.

This is what it would look like to do a front flip in 3 dimensional hyperbolic space tiled by regular right angled dodecahedron.

Created with Curved Spaces.

Flying though a tiling of regular right angled dodecahedron in three dimensional hyperbolic space. There is more of an explanation here.

Created with Curved Spaces.

Flying through Euclidean 3-space

View as a single GIF here

Flying through Euclidean 3-space

View as 4 quadrants here

This is a stereoscopic image

Source:
knotplot.com

Notes: 4
5/9/11 — 10:31pm
Filed under:
#knot
#link
#3D
#stereogram
#knot theory
#stereoscopic
This is a stereoscopic image

Source:
knotplot.com

Notes: 2
5/9/11 — 10:30pm
Filed under:
#knot
#link
#3D
#stereogram
#knot theory
#stereoscopic
This is a stereoscopic image

Source:
knotplot.com

Notes: 3
5/9/11 — 10:30pm
Filed under:
#knot
#link
#3D
#stereogram
#knot theory
#stereoscopic
This is a stereoscopic image

Source:
knotplot.com

Notes: 4
5/9/11 — 10:29pm
Filed under:
#knot
#link
#3D
#stereogram
#knot theory
#stereoscopic
A stereoscopic 3D projection of a tesseract.

Learn how to view here.

High-res
Notes: 6
4/30/11 — 3:53pm
Filed under:
#3D
#steroscopic
#geomtery
#4D
#stereogram
#stereoscopic

Cross your eyes so that the two images converge to one in the middle. Your right eye will be looking at the left image, your left at the right, you will see 3 images and the middle one will be in 3D! This is the Mathematica spikey shape, and it was the answer to the flat-land problem I set a few days ago. [my code]