How to model a ridged cone (using modifiers)? See the picture at the bottom for what I want to model.  I’m using Blender 2.8 Beta.

I was thinking an open cone (that is, bottom face removed) with some modifiers applied, and a creative texture, should do this.  But as a beginner I'm in over my head.

I was first inspired by something I had seen with the wireframe modifier, which can produce the nest-of-spikes effect on a cone.  



But it doesn’t quite work right (I could cut off the bottom using a Boolean, though) and I don’t have any control:  Make the creases shallower but still broad enough to span to the next.  With “Relative thickness” it gives points that extend past the end, but they are far too long, and again, I can’t control that separately.

Meanwhile, I was thinking the top-to-bottom scale-like ridges could be done with a modifier, as I see there are some named “Wave” and “Displace” but I can’t figure those out when I just tried it to see what happens.

The final bumpiness could be done with a bump map procedural texture, I’m sure.  I’m familiar with the concepts from POV-Ray (years ago), but looking at the node editor I was again at a loss as to how to do that.

Any suggestions, or pointers to tutorials or .blend files that contain similar features that I can learn from?
Here is a way to do it:


Create a plane, go in Edit mode, rotate on the X axis and scale it, move it a bit away from its origin on the Y axis.
Cut it in half with a vertical edge loop, give it a Mirror modifier, enable the Clipping option.
Create an empty on the same position as the plane origin.
Select the plane, give it an Array modifier, deactivate Relative Offset and activate  Object Offset, choose the empty as the Object. Choose a Count of, for example, 18. Activate the Merge and First Last options.
Rotate the empty 20° on the Z axis.
Select the plane, go in Edit mode and edit the plane mesh, move the vertices, add some vertical edge loops.
Give your plane a Subsurf modifier, add some horizontal edge loops.
When you'll be glad with the result, keep a copy, then apply all the modifiers except the Subsurf, remove the doubles, close the top with some altM > Merge.