1 January 2005

Galaxy simulation: matter clumping into filaments in a wrap-around universe

Java applets 1–5 January 2005

Nine versions of the applet, Galaxy2, written over the first five days of January 2005. Drag the mouse over an applet to add matter.

Java galaxy applet: matter and its gravity field

Version 0.01: distorts image as you draw 1 January 2005

Java applet, run by CheerpJ. Main class: Galaxy2

Version 0.02: supposed to be gravity but looks nice anyway 1 January 2005

Java applet, run by CheerpJ. Main class: Galaxy2

Version 0.03: great when you get it really going! 1 January 2005

Java applet, run by CheerpJ. Main class: Galaxy2

Version 0.04: antigrav, grow your own bacteria 1 January 2005

Java applet, run by CheerpJ. Main class: Galaxy2

Version 0.05: mad mould 1 January 2005

Java applet, run by CheerpJ. Main class: Galaxy2

Version 0.06: working gravity, fudged 1 January 2005

Java applet, run by CheerpJ. Main class: Galaxy2

Version 0.07: proper gravity at last, I think 1 January 2005

This version
2005-01-03


ood2 is now pre-multiplied into dirx and diry
Java applet, run by CheerpJ. Main class: Galaxy2

v6 2 January 2005

Java applet, run by CheerpJ. Main class: Galaxy2

Version 0.08: perfected gravity, slow n^4 method 5 January 2005

This version
2005-01-03

ood2 is now pre-multiplied into dirx and diry

took out wrap-around from calculations
Java applet, run by CheerpJ. Main class: Galaxy2

Basic gravity simulation 4 January – 12 November 2005

This is a simple animation framework set up for doing the galaxy simulation. It is a Win32 C++ program built on the FFTW library; each version keeps its notes in a comment at the top of Pattern.cpp.

The simple framework: mass, velocity and force fields side by side

Simple framework 4 January 2005

uses fft fluid solver with gravity forcefield

todo:

use forward projection instead of sime-lagrangian lookups

Proper calculation, O(n^4) 5 January 2005

In this version:

  use forward projection instead of sime-lagrangian lookups
  combine ood2 lookup with dirx and diry

Past mass lookup 24 March 2005

This version:

  Made gravity travel at the speed of light instead of infitiely fast

  Method:

    Store previous mass frames
    Instead of using current mass frame for each pixel's calculation use a past mass
    frame depending on the distance of the pixel from the one it is affecting.

  I'll call the technique Pass Mass Lookup

Some different values followed on 31 March.

Proper working gravity at last 4 April 2005

pprizm (prizm ep) - i miss u already (benbecular label, scotland, techno)

This version:

  woohoo - looks like i can do gravity using fft

  I've had to negate the gravity strength and swap the x and the y lookups for some unknown reason

Then a nice single galaxy the same day, a good interface and various speed improvements on 5 April, “all working, happy” at 512 and at 128 on 11 May, and universal expansion added on 12 November.

Source

Using FFT to simulate gravity 5 April 2005

Operation
-

The universe is DIM x DIM, and DIM must be a power of two.
The universe is tiling (wraps around at the edges)

(because it uses &(DIM-1) as a quick way of wrapping around,
and because the FFT expects powers of two (i think) )

The universe is represented by a mass and an x and y direction (velocity)
for each pixel in a DIM x DIM square.

The gravity calculation involves calculating the force on each pixel
from the rest of the universe:

  for each pixel A
  {
    force_x = 0
    force_y = 0

    for each pixel B except A
    {
      force_x += horizontal force on pixel A of pixel B
      force_y += vertical force on pixel A of pixel B
    }

    //  (force_x, force_y) is the total force on this pixel
    //  from the rest of the universe
  }

After the force is calculated it is used to modify the velocity of the pixel.

Because the universe wraps around, each of the other copies of the universe
has an influence.

  for each pixel A
  {
    force_x = 0
    force_y = 0

    for each tile
    {
      for each pixel B except A  //  i think you need to include A in all galaxies apart from real one?
      {
        force_x += horizontal force on pixel A of pixel B
        force_y += vertical force on pixel A of pixel B
      }
    }

    //  (force_x, force_y) is the total force on this pixel
    //  from the rest of the universe
  }

The force is a convolution of the mass array and the gravity force array.

To move the mass based on the force, start with an empty array (zero's)

  NEW_MASS = zero array

  for each pixel
  {
    M,DX,DY = pixel's mass and velocity

    NEW_X = pixel's x position + DX
    NEW_Y = pixel's y position + DY

    Place mass and velocity into NEW_MASS with sub-pixel accuracy
  }

To do a fast convolution of A and B (both power of two
The full sequence is:

  Create gravity lookup tables LOOKUPX and LOOKUPY

  each frame
  {
    FORCE_X = convolution of LOOKUPX and MASS
    FORCE_Y = convolution of LOOKUPY and MASS
    Apply FORCE_X,FORCE_Y to MASS
  }






  Create gravity lookup tables LOOKUPX and LOOKUPY
  Calculate fft of LOOKUPX as V0
  Calculate fft of LOOKUPY as V1

  each frame
  {
  }


The gravity force array can be precalculated and saved off.






Notes
-

. Horizontal and vertical bias because of the grid nature of the universe
  . Horiz and vertical streams coming out of tiny heavy galaxies when matter should be fired out in all directions
  . Long thin galaxies form which suspiciously travel exactly in the x or y dir

Out-takes January – November 2005

Interesting visual effects when things go wrong. Two of them record steps towards the FFT version. From 6 January:

003:

  use forward projection instead of sime-lagrangian lookups
  combine ood2 lookup with dirx and diry

004:

  use fft image convolution to calculate gravity (avoids n^4 calc and reduces it to n^2)

And from 31 March, “broke it whilst putting in FFT”:

007

trying FFT for gravity convolution

just put init_fft in, need to calculate kernel etc.

Source

3D visualisations 13 November 2005 – 23 May 2006

A 3D view of the simulation in November 2005, then a 2D galaxy with a 3D timestack in May 2006, with improvements the same day.

Source