The Pattern Breathing

Here are some GIF movies of the pattern "breathing".

In the next movie, I have put a sphere in the center so you can easily follow the motion.

The above movie might be called a "half-cycle". The motion begins as a hoop, flexis open, closes back to a hoop and then repeats.

However, we know that the pattern can pass through itself. (This is shown in my movie which shows the pattern evoluting on a torus. This was also discovered using a wire model at Sequoia meeting II.) So the following movie might be called a "full-cycle".

The pattern is seen opening into one orientation, closing back into a hoop (at which point it passes through itself) and then openning up again but in a differnt orientation. The significance of this is explainned in the section called "The pattern generates the duo-tetrahedron."

Her are two other movies...

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