Toroidal Universe N-Body Simulation

A first test of a N-Body Simulation of a Toroidal Universe with 25k particles using Barnes-Hut and 26 adjacent Universes at the side of each part of the cube. The simulation was carried during an 8 hour period on a single machine to test for errors with 8k iterations.

"IN MATHEMATICS, A DOUGHNUT SHAPE is known as a torus, the three-dimensional generalization of a ring. A ring lies in a single plane; so topologically speaking there is one closed path around it that lies just outside it (a loop around the ring). Because a torus has one more dimension, you can travel along closed paths around it in two perpendicular directions. If you imagine a doughnut on a plate, one of these is a larger loop around the periphery, parallel to the plate, and the other is a smaller loop through the hole, toward and away from the plate. The generalization of a torus, any closed curve spun in a circle around an axis, is called a toroid. Curiously, there are genuine scientific theories that the universe is toroidal. A flat two-dimensional planar geometry -- a square, let's say -- can be transformed into a cylinder by identifying the far left side with the far right side, essentially gluing the two sides together. If an object travels far enough to the left, it ends up on the right. Something moving continuously to the left or right would experience the same region again and again in periodic fashion, like the animation loops common to cartoons from the 1960s and 1970s. Used to save time and effort, animation loops occur when the characters pass by the same background scenes again and again. An even more intricate arrangement links the extremes of all three spatial dimensions into a kind of "über-doughnut." Imagine space as a colossal cube; these connections would equate to the left and right, top and bottom, and front and back faces. Such a layout, a generalization of the torus with a three-dimensional instead of a two-dimensional surface, would be hard to visualize. Paradoxically, it merges a straightforward "flat" geometry (in the sense that parallel straight lines remain straight and parallel) with a mindbogglingly complex topology." by Paul Halpern Cosmos Magazine

Category:

Science & Technology

Tags:

• N-Body Simulation
• Barnes--Hut
• Toroidal Universe
• doughnut universe

[jdogsful]

if it had an extra doughnut and an extra cube at each side and each of those cubes had a cube at each side id probably have to agree