A Barnes-Hut Simulation is an N-body simulation of gravitational interactions between point particles using the Barnes-Hut algorithm.
This simulator runs a simulation of the gravitational interactions between an arbitrary amount of bodies/points (tested up to 100k particles, see below) in a 2D field:
A Barnes-Hut Tree sub-divides the space by quadrants, providing a large speed-up by approximating particle interactions at long distances:
Open main file index.html with browser Some screenshots are also in repo.
With Brute force :
O(n^2) calculations (exactly
(N-1)*N/2 actually), roughly 125k force calculations for N=500.
With Barnes-Hut tree calcualtions, it'll be
With a low number of bodies N < 50 or so, a slightly streamlined brute force is more efficient than a Barnes-Hut tree, but as N increases, the efficiency increases dramatically: With Theta = 0.5, roughly 50% gain for N < 500, 80% for N < 1000, reaching up to 90% beyond.
With 10k bodies it takes around 0.5~0.8 seconds to compute a step, and 0.1-0.3 seconds to display it on the canvas.
Debug using the console (older image):
Basic framework set up, basic graviation working with forward euler and leapfrog integration.
O(n^2) for all bodies. Real-time for roughly N < 500
Barnes-Hut calculation implemented and working. Real-time for N > 1k etc.
Efficiency information is shown in real-time to the right of the canvas.
Following examples testing with Theta=1 (not accurate) Example with 1,000 bodies.
# Bodies: 1000 # Force calculations per step: 32457 BN TREE - Depth: 11, # Nodes: 1544, # Leafs: 891 BN Tree O(nlogn)  Efficiency vs Brute Force O(n^2)  96.75% Efficiency vs Half Brute Force O(n^2)  93.50%
With 5,000 Bodies
Bodies: 5000 Force calculations per step: 623195 BN Tree Depth: 13 Nodes: 8681 Leafs: 4979 Number of Calculations BN Tree: 623195 Brute Force: 12497500 Speedup : 95.01% Time per step Compute : 752ms Display : 636ms
With 10,005 Bodies
# Bodies: 10005 # Force calculations per step: 383004 BN TREE - Depth: 13, # Nodes: 17368, # Leafs: 10005 BN Tree O(nlogn)  Efficiency vs Brute Force O(n^2)  99.62% Efficiency vs Half Brute Force O(n^2)  99.23% Time to compute step : 615ms Time to display step : 156ms
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