My Math Forum Fractal dimension of snowflake falling into black hole

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 February 17th, 2014, 11:13 AM #2 Senior Member   Joined: Jan 2013 Posts: 209 Thanks: 3 Re: Fractal dimension of snowflake falling into black hole After thinking more about it and the various small simulations of the pieces of math (interactive visual is best), I've simplified that mess of details... Capacitor, inductor, and resistor in combinations of series and parallel circuits, time symmetric as an undirected graph with scalar edge weights constrained to each range 0 to 1 and per node sum to 1, which is called a symmetric Stochastic Matrix, are descriptions of solutions to how the edge weights can be. Each node in a clique has the same weight with each other node in that clique, which can be modified by adding a multiple of any path which covers all nodes once and has the same weight on each of those edges, and can also be modified by a multiple of any clique cover, and recursively in any clique of even size (boson because it slides easy) without consideration of whats outside the clique there can be recursive clique cover by choosing any pairing of the nodes in the clique, or if the clique size is divisible by x and y you have a clique cover x cliques and y loops around them (or the reverse y and x), or anything else proven equal to NP Complete will be found in a symmetric stochastic matrix. A rotating black hole (quasar, subject of penrose process) is a loop of cliques which each overlap the next and previous on most of the nodes and gradually as they get farther away (angle on complex unit circle) the cliques overlap eachother on less nodes. If you circuit in series to all those partially overlapping loop of cliques then you have edges to all of them and will get the same sum regardless of its angle because its (biggerSetOfNodes choose cliqueSize) as pascals triangle calculates. If you circuit in parallel you will see the rotating black hole as an oscillation because you can only see part of it at a time. Series is a timeless concept that means AND. Parallel is a timeless concept that means OR. Resistor is a timeless concept that means 1^(1/2) which has the solutions -1 and 1 in the context of zigzagging back and forth from the top of pascals triangle. Branching to both childs of a pascals triangle cell is series because series is AND. They must both be crossed. The rows of pascals triangle are parallel because as long as you move left the same number of times (and therefore also right the complement number of times), you arrive at the same cell on a chosen row number. The leftmost diagonal direction is all 1s. Next is counting 1 2 3 4... Next are the triangle numbers which are the quantity of edges in an undirected graph. Next is the number of triples, which counts faces on a sphere viewed as 4 points and 4 triangles between them. Pascals simplex proves this is the topology of n-sphere as you count higher. A clique is a cliqueSize-1 sphere which is how many edges each node in the clique has. A single node (clique size 1 if we were not doing it as undirected graph so no self edges) is a 0-sphere which has the equation x^2 = radius^2. A 1-sphere has the equation x^2 + y^2 = radius^2. You keep adding x y z ... as many sphere dimensions as you want. The 2 nearly touching metal plates in a capacitor are parallel of many points on each plate. The coils of an inductor are parallel in how field doesnt care which time around its just a field in that general area. Those same coils are series in how each particle must cross every coil, literally the series of points in the wire thats coiled. Pascals triangle branching left and right repeatedly is a resistor in how it generates bell curves by random movement. Anything which had solved constraints while using an edge to any such randomness will find their constraints have that much error added, and since by definition the constraints are always solved (else they wouldnt be constraining the stochastic matrix) anything which causes them not to be solved resists flow through that path. I'm not saying we can efficiently simulate every part of this, or maybe we can, but the point here is the equation of parallel and series circuits of inductors capacitors and resistors describes these edge weights when the undirected graph is viewed as parallel, series, and resistors in a multiverse of possible ways. For example, the rotating black hole is farther away from those who view it as in total multiplied by a smaller fraction, compared to others who only solve their constraints when its larger or when their edges to it are only to some parts (edge value is less to/from those others in the loop of partially overlapping cliques). The equation is repeated different ways for inductors capacitors and resistors in parallel and series at http://en.wikipedia.org/wiki/Series_and ... l_circuits and that equation in general form is self^(-1 or 1) = x^(-1 or 1) + y^(-1 or 1) + ... (the same exponent for all of them, so sum linearly or use sum of inverses) The penrose process acts on the loop of partially overlapping cliques to cause the angle (which of the cliques on the loop?) to move slower (as others with varying edges to the rotating black hole must sync with else be out of sync with who does the penrose process), or if outside observers have parallel connection to the penrose doer and the rotating black hole then by enclosing surface whatever happens inside the surface has no effect on the outside observer because it only changes edge weights inside that set of nodes. Outside observers only see the rotating black hole slow down after the doer of penrose process gets far enough away from it to be entangled with the outside observers edges. By entangled I mean that randomizing 1 will cause a balancing change in the other, but not necessarily any specific balancing change since there are many solutions in a symmetric stochastic matrix. The universe can be viewed as a clique cover where edge weights in each clique are 1/(cliqueSize-1) or path covering all nodes and 1/2 edge weight, which is an NP Complete string, or any other view of NP Complete of which many have been proven interchangible. But how do I draw it on screen? I'll stick with the original simple goal of simulating ball lightning (and later fractal snowflake). The sphere surface will have to form on its own somehow, but at least now I know to use capacitor inductor and resistor in parallel and series circuit equation, double slit being parallel before the slit (choose any or some of each) and series through it (choose both) or the opposite which is series before the slit (conserves flow since it must go through all of them individually) and parallel through it (choose either slit or a fraction of both, total flow is series with before it split and after it hits back wall). In the middle it may be a combination of series and parallel, but its series to the extent you detect it on back wall, so a series of smaller circuits each constrained to conserve flow. Delayed Choice Quantum Eraser is a resistor where its observed in the future because such observation changes a parallel (could have gone either way(s)) to a series (the universe is only consistent if it happens as observe here in the future) so the earlier double slit gets its parallel and series swapped (remember I said it could be either way before vs during the slits), and exactly how it keeps swapping recursively I'll have to explore in simulation but the general way it puts a bell curve statistic on back wall is pascals triangle (bell curve by repeated coin flips) and wave through both slits statistics on back wall is rotation by capacitor (which I think of as xor in the time view and inductor in how it resists change to the charges on each metal plate). The entire data structure is an undirected graph with scalar weights between each pair of nodes. Anything else would be to paint it onto a 2d screen of pixels and get the mouse to drag things around, which is really hard since you can't have 2 dimensions unless you derive them as mapping combinations of nodes and edges to parts of the screen.

 Tags black, dimension, falling, fractal, hole, snowflake

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