What do you call a system (like mine) that exhibits emergent physics-like behaviour from particles only described by their position? I built a computer simulation of a 2D space which contains particles of only two types: attractive and repulsive. The particles only have an X and Y coordinate. The repulsive particles are repelled from all other particles, while the attractive particles are attracted to all other particles. Each frame, the next position of each particle is calculated based on the attractive and repulsive forces of all other particles, with something like the inverse square law used to decrease the influence of faraway particles.
When I tweak the forces just right (and add a few minor hacks, like a force pulling everything to the centre) I find that higher-level features emerge in the system, such as clusters of attractive particles surrounded by a bubble of empty space, and repulsive particles filling the remainder of the space. The cluster will tend to be closer to one side of the bubble and so will move in that direction. Resulting in a tear-drop like shape. These patterns resemble the behaviour of physical particles, even though the individual particles in my system do not have properties such as mass, speed, and direction. The emergent particles will collide with each other, bounce off of each other, and sometimes merge and split. All of this behaviour is emergent.
I am curious if a system like this has been studied before, and if so, what it is called. I am also interested in whether this system might be of value to study further, as it exhibits emergent behavior that arises from the interactions of simple components.
So far for me this has been a fun experiment rather than proper science/maths but I would appreciate any insights or references to related concepts or approaches that might help me better understand this system.
I have also tried a 3D version, but although this exhibits similar behaviour it is more difficult to see what is going on.
I've also asked on the math StackExchange as it seemed to straddle math and physics.
I have some videos on a YouTube playlist
Example image from a simulation

UPDATE:
To make clear, my question is not regarding the exact details of this simulation, just whether this sort of system is known about [a system of emergent "physics" where the low level particles only have a position]
UPDATE 2:
The only state of the system is the X,Y coordinates of the low level repulsive and attractive particles. The next frame is entirely determined by the positions for these particles. What you see in the screen shot is attractive particles forming clusters surrounded by tear-drop shaped bubbles where the repulsive particles have moved away. I don't think it is obvious that this behaviour would arise, but seeing the videos/screenshot you can kind of see why it happens.
I think normally for a particle simulation you would need the state to include the speed and direction of each particle.
Of course I am aware that the "physics" that is emergent here is fairly weird physics and I'm not pretending that this is the physics of our universe.
If no one knows what this system is called, perhaps someone can help me find better lingo to describe it. Is it correct to say this is physics without time derivatives?
In essence the pseudo code for the system is as follows
let the system contain a set of points some of which are 'attractive' and the others 'repulsive'
so each point has only an X coordinate, a Y coordinate, and a boolean Type
let the function f be something like the inverse square law (actually in the 2D example it works better with an inverse cube law)

calculate the next frame by running the following:
for every point p
    for every other point q
        apply f to the vector p->q to get the vector v
        if p is an attractive point
            set p’s new position to be p + v
        else
            set p’s new position to be p - v

UPDATE 3: If more clarity or detail is needed, please be very specific about is required.
 A: 
These patterns resemble the behaviour of physical particles, even though the individual particles in my system do not have properties such as mass, speed, and direction.

Your particles do have mass, speed, and direction, though you may not have intentionally specified them. The fundamental unit of time in your simulation is the inverse frame rate $\delta t$. The velocity of a particle is given as usual by displacement over time. The mass of the particle is hard coded into its response to the net force on it due to the other particles.

The emergent particles will collide with each other, bounce off of each other, and sometimes merge and split. All of this behaviour is emergent.

One of the very beautiful aspects of physics is that even if the fundamental laws are very simple, the subsequent behavior (especially of collections of particles) can be very rich indeed. For example, if you gave the force between particles a long-range repulsive / short range attractive character (see e.g. the Lennard-Jones potential), you may be able to observe condensation and vaporization.

I am curious if a system like this has been studied before, and if so, what it is called. I am also interested in whether this system might be of value to study further, as it exhibits emergent behavior that arises from the interactions of simple components.

It sounds to me like you've implemented a classical molecular dynamics simulation. Such simulations are quite interesting despite their comparative simplicity, and have been in existence since the 1950's. The field of computational physics has given us a very broad range of simulations which are useful for a wide variety of different applications in every conceivable branch of physics; you may be interested in delving deeper into some of them.
