03-24-2019, 05:23 PM

Good afternoon!

I am working on various ways to twist and squish a Seirpinski Tetrahedron.

Background: 1st iteration of Sierpinski Tetrahedron, with four axes drawn from the center of the figure through the smaller tetrahedra.

Foreground: Each tetrahedron has been rotated 50 degrees counter-clockwise on its axis, and then slid along that axis towards the center until they just touch.

I want to give a proper IFS treatment of this arrangement using different angles. The problem is, I don't want to have to tweak all four of the smaller holons separately every time I want to make a small change. Is there a way to adjust all four copies at once? That is, so that turning one turns them all on their own different axes.

One way I am picturing it is to start with a tetrahedron constructor, then add a holon that scales it, moves it, and rotates it move and rotate it along the z axis. But then we want three more copies with the same rotation and distance from the center, each at a tetrahedral angle (~109 degrees) from the first one.

But again, (here's the catch) how do we get the three copies to follow the first one when it's moved, so the whole arrangement is easy to tweak.

Is there a way to build such a thing?

Chris Jones

Eagle River, Alaska

I am working on various ways to twist and squish a Seirpinski Tetrahedron.

Background: 1st iteration of Sierpinski Tetrahedron, with four axes drawn from the center of the figure through the smaller tetrahedra.

Foreground: Each tetrahedron has been rotated 50 degrees counter-clockwise on its axis, and then slid along that axis towards the center until they just touch.

I want to give a proper IFS treatment of this arrangement using different angles. The problem is, I don't want to have to tweak all four of the smaller holons separately every time I want to make a small change. Is there a way to adjust all four copies at once? That is, so that turning one turns them all on their own different axes.

One way I am picturing it is to start with a tetrahedron constructor, then add a holon that scales it, moves it, and rotates it move and rotate it along the z axis. But then we want three more copies with the same rotation and distance from the center, each at a tetrahedral angle (~109 degrees) from the first one.

But again, (here's the catch) how do we get the three copies to follow the first one when it's moved, so the whole arrangement is easy to tweak.

Is there a way to build such a thing?

Chris Jones

Eagle River, Alaska