For a constructive solution, in which different parameters can be set, a self-defined geometry is useful. I myself would take a sphere with holes as a base. (triangulation according to an algorithm by E. Hartmann)
Triangulation sphere with holes
The positions of the holes can be defined e.g. via quaternions. Quaternion - Axis, Angle Visualization
Then you can attach the tentacles. Inner Geometry (Triangulation)
Example
https://hofk.de/main/threejs/Triangulation/InnerGeometrySphereCylinder.html
I did it for cylinders. You can use a function of the outside line instead of the cylinder with the linear outside line. Then you have to calculate the normals a little more complicated. But it’s certainly not that hard.
However, you may be able to take a CylinderBufferGeometry and change the distance of the vertices to the centerline (radius) according to a function.
There are many variants. 
Inspirations:
Addon to create special / extended geometries
Addon. Produces almost infinite many time-varying geometries with functions