The sphere is the surface that needs to be deformed by the presence of the cones. The surface can't be modified in any way, we need to stick to its topology and shape. We want to do this dynamically just using a displacement map but of course we don't want to sculpt the details by hand, as the animation might change at any time and we would have to re-sculpt again.
The cones are growing from frame 0 to 60 and moving around randomly.
I'm adding a for each connected piece and inside the loop adding an edit to increase the volume of the original cones a little bit.
Just select all in the group field, and set the transform space to local origin by connectivity, so each cone scales from it's own center.
Add a vdb from polygons, set it to distance VDB and add some resolution, it doesn't need to be super high.
Then I just cache the VDB sequence.
Create an attribute from volume to pass the Cd attribute from the vdb cache to the sphere.
To visualize it better you can just add a visualizer mapped to the attribute.
In shading, create an user data float and read the Cd attribute and connect it to the displacement.
If you are looking for the opposite effect, you can easily invert the displacement map.