Weird fluid with strange attractors as particles…

Consider the Sprott attractor given by KNXVQUEXYETWOOSGNSBDMHTMCFLNGP

Imagine very many tiny particles, each of them shaped like this attractor. (which is not technically hard to do, just add a prefactor and a postfactor and the attractor can be scaled to any size). One way of thinking about the attractor is a probability distribution in \mathbb{R}^{3}. Suppose that so long as the sum of the probability distributions is less than, I don’t know, to pick a real number at random, say 2\gamma/3, where \gamma is the Euler-Mascheroni constant. These particles will interact in a very odd way compared to a fluid composed of atoms. Which means that you could have many of these particles (let’s assume that we scale it down \frac{1}{4096}). in the same space at once so long as the sum of the probability distributions at a some given point was less than \gamma

We could try a range of sizes, perhaps. What I want to impress on you is how very oddly the fluid particles interact with each other, for they don’t encounter resistance until the sum of the probability distributions of each is 2\gamma/3, though it would make sense that their rate of movement at a point would depend on the ‘evanesences’ — less evanescent intersecting materials would move through each other more fluidly.

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packing strange attractors

This is a lark, but it’s a fun one. Suppose you have a lot of different polynomial strange attractors (like the ones I have previously posted to their blogs). Suppose that they’re made out a material such that so long as the sum of the probability distribution function between the both is less than, say, one ninth, they can intersect. What packing properties would it have? If you had a lot of them, how would a fluid composed of strange attractor shaped particles behave? 

lacunary functions

There is a point of view that I want to bring to the study of lacunary functions. It’s a little weird. It goes like this: we treat the lacunary function as the mapping of the night sky — a hemisphere, to a circle. The lights on the horizon — which correspond to the singularities on the horizon. Roots are stars.