Algodoo

How can two particles ( purple and maganta )
attract each other, allthough they only have the chance to create
and throw balls, with repulsion?

1) In a circle around the purple particle a yellow outgoing ring of balls
as well as an ingoing cyan ring of balls is created, satisfying
conservation of momenta, as each yellow ball has opposite
momentum to his cyan partner-ball.

2) If a yellow ball finds an interaction-partner, which is here
the magenta particle, it is deleted instantly as well as its
cyan partner-ball.

3) All remaining cyan balls hit the purple particle. If no cyan ball is missing,
the hits of all cayn balls result in a 0-vector acting on the purple particle,
so it stays where it is. We can say: their actions extinguish each other.
But if some cyan balls are missing, then the cyan balls on the opposite side
of the missing ones push the purple particle into the direction of the missing
ones.

4) From outside, without knowing or sensing any yellow or cyan balls,
one would only see the attraction of the two particles.

5) Start the simulation. Be patient, the first "rings" will start after
about 4 seconds. Now Move (M) the magenta particle into the range of the
yellow balls and watch how they are destroyed as well as their cyan
partner-balls.

6) Steer the purple particle to the orange square only by using the
"attraction by repulsion" power of the magenta particle and the rings of
balls of the purple particle.

7) In real physics, there is not just the action of the magenta particle
on the purple particle, but also vice versa, so its an "Interaction",
as the purple particle also acts on the magenta particle. It would be too
confusing to establish this also in this algodoo-scenario, and to begin to understand
the model, one side of the action is enough to be animated. Allways remember
that this is just a model to explain how attracting interaction could "work".

8) About momentum-conservation
In the moment where balls are deleted due to their limited "time to live", the sum of momenta is no more conserved. I had to implement this limited lifetime in order to keep the simulation smooth and the number of balls small. If one would use the Inter-action, as denoted in 7), the other particle would receive precisely the same amount of momentum in opposite direction, so momenta are conserved then.