The topic of the last post in this series

Blender – complexity inside spherical and concave cylindrical mirrors – I – some impressions

Blender – complexity inside spherical and concave cylindrical mirrors – II – a step towards the S-curve

Blender – complexity inside spherical and concave cylindrical mirrors – III – a second step towards the S-curve

was the construction of a metallic object with basic similarities to the “S-curve” of artist Anish Kapoor. Our object was a bit more extreme than the artists real object; we had a smaller curvature radii in two dimensions and on the outer ends our surface approximated a half circle boundary curve. We therefore could expect multiple reflections of light rays on the **concave** side(s) of our virtual object when applying ray tracing.

At the end of my last article I already presented some images of the reflection of a far distant horizontal line marked by a sun close to the horizon at dusk or dawn. In this article I am going to add some simple objects – a small red and a small green sphere at varying positions. Plus a point like light source. I take some shots with the virtual Blender camera form different angles and with varying focal length. I present the results below without many comments.

What we see is a rich variation of patterns and figures. Mathematically it is all the result from a single and simple mapping-operation. Each operation maps one point on our surface to another point on the S-curve (or on a hit sphere). The points are given by millions and millions of light rays which in the end reach our virtual camera from different angles. The basic message is:

Simplicity can create a complexity which or brain would not predict without some deeper analysis. And a complex apparition may be based on simple rules and the selection of special circumstances.

So, besides many other philosophical aspects Mr. Kapoor’s “S-curve” reveals a very fundamental idea in physics, certain branches of mathematics and in information theory.

# Reflections of a horizon line

# Reflections of a horizon line and a red sphere

# Reflections of a horizon line, a red and a green sphere

Note that the concave side of the S-curve gives us a first idea about what we can expect from a full half-sphere where even more reflections on the surface are possible before a light ray reaches the camera.

But, in my next article

Blender – complexity inside spherical and concave cylindrical mirrors – V – a video of S-curve reflections

I am first going to produce a movie of objects moving in front of the concave part of the S-curve.