Say I want to create a field of objects using Unity's particle system, except I want to use my own particles instead of Unity's default particle. How can I create such a custom particle system?
Is there a way to do this without using the particle system? I would like the objects to move in a similar way (that is, randomly).
You are able to change the material that a particle system emits, which should allow you to have a particle system emit materials with custom textures.
You will first need to create a new material, by going to assets > create > material.
On your new material, go to the inspector window and click the dropdown shader menu and select particles. I chose additive to test this, but as long as the material allows you to add a texture you should be fine.
When you have your new material, you can then change what is being emitted by the particle system to your new material. Select your particle system in the hierarchy viewer and go to the inspector view.
Under particle system you should scroll to the bottom section called renderer, open the section up and click on the small circle to the right of default-particle in the material property.
Simply select your new material from the popup menu and you should be good to go.
Here is a link to some useful screenshots that might help: https://imgur.com/a/venMr
Hope that helps!
[EDIT] - If you want to use 3D objects in the particle system then you can do that too.
Go into the inspector view and back to renderer, from there change render mode from billboard to mesh You can then select different 3D meshes from the mesh property.
In terms of 3D objects the particle system is generally designed to emit meshes only, although if you want to emit your own objects there are plugins available for purchase on the Unity store.