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README.md

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+
+strong nuclear force (quark confinement)
+the force between particles stays constant
+no matter what distance
+
+
+spring universe (hooks law)
+- when particles are far apart, it gives a huge attractive force
+
+
+BAND
+- when particles are far apart, it gives attraction,
+  but when particles are too close, it gives repulsion,
+  so you have this "band" in which the force kinda drops off... and is negligable
+- molecular dynamics:
+  - when far apart, you have very small attractive force
+  - when close, strong repulsive force
+
+
+Galactic Gravity
+- instead of newtons 1/r^2, use 1/r
+- orbits around a heavy body will move at constant speed
+  reg
+
+
+
+Boids
+- don't crowd neighbours
+  - neighbours that are close have repulsive force
+- alignment
+
+
+What about different types of "masses"?
+e.g. something like charge, or perhaps something weirder?
+
+====Implementation====
+
+Should I track momentum or velocity?
+Since I have constant mass particle,
+I can always compute velocity easily.
+
+# Time and Evolution
+Decoupling simulation step from `dt` given by the browser.
+
+# Global attributes
+- net force (should be very close to 0)
+- net momentum (should be very close to a constant)
+What else?
+- average kinetic energy (temperature?)
+- center-of-mass (should be constant)
+
+- WTF potential energy? How to calculate that? Probably
+  always different for each of the systems? Does it always make sense?
+
+
+# Camera & Culling
+
+- zoom & pan
+- render only those particles that are on the screen
+  - note that this is gonna fuck up the trails, but whatever
+
+
+# Brushes
+## Spawning
+- spray paint - bunch of particles near each other but with non-zero initial velocity
+- single heavy click brush spawning particles
+- brush that spawns particles orthogonal to the center of mass
+
+## Filtering
+- delete particles in mass range
+- delete particles in region
+
+## Mapping
+- change mass of all particles based on a function.
+
+## Reduce
+- Replace particles in a region by one particle that has combined mass
+
+# Local Attributes
+- follow a single particle and highlight it, name it, display its attributes
+
+- Select a square/circle s.t. all particles within it
+  are now tracked... or perhaps those that enter/exit it?
+
+
+
+# Dimensions/Layers?
+What about having quantities such as a `phase`?
+Where basically particles of different phases don't interact... but then we could change phases of particles, and suddenly there is interaction etc...
+
+
+
+
+# Symplectic vs Explicit Euler
+Suppose we have `(pos0, vel0)`, and we have `dt`. We compute `acc` (acceleration).
+Then the enxt state is:
+- Explicit: 
+  ```
+  (pos0 + dt*vel0, vel0 + dt*acc)
+  ```
+- Symplectic:
+  ```
+  let {
+    vel1 = vel0 + dt*acc,
+    pos1 = pos0 + dt*vel1,
+  .
+    (pos1, vel1)
+  }
+  ```
+  I have no idea why symplectic works...
+  Does it work only for some systems or all?
+
+
+
+# Energy
+- Kinetic Energy is the energy of motion...
+- Potential Energy is the energy of position/configuration (relative position? idk...)
+
+
+Compute? Potential Energy is integral of force over distance...
+
+Hmm. Let's have `f : M -> R` the "potential".
+The force field that's generated by `f` is `d(f)` - but actually... the gradient?.
+But given a force field, how can we attempt to
+compute the potential energy? Atleast on the trajectory of the particle...
+
+There's no unique solution... so let's say we spawn a particle, and give it potential of 0.
+
+Then the acceleartion field tells us in which direction to move. I guess we're computing an integral over some 1-form. How do we get the 1-form?
+
+It is at a point, the inner product of the infinitesimal velocity with the infinitesimal force...
+```
+<dv|df>
+```
+
+
+
+
+
+
+# Angular Momentum?
+
+
+What if our basic element would be like "rods" of two particles where the constraint is that the distance between them is fixed. Then we could naturally have
+angular velocity etc...
+
+