Cube

silviana amethyst

Equation

\[ x^6 + y^6 + z^6 - 1 \]

Properties:

Some story

The `cube’ is not really a cube. It has no corners, but instead is smooth. Taking the power of the variables to infinity produces a cube, and is related to the various metrics for distance.

Random projection is all good, and no need for a custom bounding sphere. Just let ’er rip.

Funnily enough, if you decompose a sphere you get a regular polyhedron, but you don’t with this.

Bertini_real input files

input

CONFIG
tracktype: 1;
randomseed: 2;
imagthreshold: 1e-4;
printpathmodulus: 0;
END;
INPUT

variable_group x1, y, z;
function f1;
x = x1+1;
f1 = x^6 + y^6 + z^6 -1;
END;