Bryce 3D (An Epitaph)

In 1997, the software department of our local book store sold heavily discounted copies of the Raytracing program Bryce,
because they had accidentally ordered Mac versions and were selling only Windows software. I purchased a copy, not knowing what this
would get me into.

Catalan

I had been making images of minimal surfaces the past year with Mathematica, and the 3D graphics of Mathematica could be first exported into Autocad DXF files, and then imported into Bryce.

Chm

Bryce is primarily a landscape renderer. The tools let you create terrains, and it comes with a sophisticated texture editor that lets you literally compose all kinds of textures for your objects.

Having abstract mathematical shapes in (somewhat) familiar landscapes seems to stretch our minds just right.

Cg

In 1997, computers were slow. Most images had to be rendered over night, to get screen filling sizes. And these were screens from 1997, too.

Tortor

The user interface of Bryce (by Kai Krause and Eric Wenger) was revolutionary, and still leaves not much to be desired today. In 1999, Bryce reached its high point with a a vastly improved texture editor. Then the decline began. Fist, it was sold to Corel, and then to DAZ 3D.

Riemann

The current version is Bryce 7, and does not work with recent Mac OS X versions. In runs under OS X.6, but is quite unstable, preventing me to rerender the old files to proper sizes.

Blackhandle
This has been a lot of fun.

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Reflections (Spheres I)

DSC5479

Large scale mirrors like the surface of a lake are awe inspiring. They simultaneously create complexity and
order. The order comes from the inherent symmetry, and the complexity from subtle differences between original and
mirror image.

Things get considerably more complicated when the mirrors are curved. The Cloud Gate sculpture by Anish Kapoor (the Bean) in the Millennium Park in Chicago is a popular example. The multiple reflections create an immediately surprising chaotic richness of the reflection: Taking one step to the side changes the appearance of the reflection dramatically. But the sculpture also extends and therefore enriches the architecture.

DSC 6142

Motivated by this, I began to experiment with the spherical mirrors, spheres being the simplest curved shapes.
For multiple spheres touching each other there is a surprising phenomenon that is best understood when we begin with seven spheres of equal size, one at the center, and the remaining six surrounding the central sphere symmetrically. Complete this configuration by adding two planes that touch all seven spheres. Now pretend that the two planes are in fact also gigantic spheres. Than these two and the central sphere all touch the remaining six spheres, which in turn form a chain where consecutive spheres touch.

Soddysimple

It turns out that this picture is not just an approximation that only works in the ideal situation shown above where the big spheres are planes, but in fact works for spheres of any size. This is the content of Soddy’s theorem.

Soddy2

To turn this into some sort of virtual sculpture, it is best to make just one of the spheres a plane. Then place two spheres onto the plane so that they touch. If you continue placing more spheres onto the plane so that they also touch the two initial spheres and the previously placed sphere, they will form a chain of six spheres of which the last again touches the first.

Soddy0

Now imagine these being really large, reflective, slightly translucent, and illuminated with colored light sources. You might see something like this:

Soddy

This is the first of a series of images featuring ray traced spheres.