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Trying to animate an extrusion in 3D using curves generated by an equation over time.

I can create a 3D spiral pattern using python and animation nodes but how can I extrude the curves so they vary over time and in 3D?

The Python code I'm using is:

import math

x1 = a*math.sqrt(t)*math.cos(t)
y1 = a*math.sqrt(t)*math.sin(t)
z1 = -t

x2 = -a*math.sqrt(t)*math.cos(t)
y2 = -a*math.sqrt(t)*math.sin(t)
z2 = -t

position1 = Vector((x1,y1,z1))
position2 = Vector((x2,y2,z2))

See attached animation of what I have:

Animation

The image I'm trying to recreate is the Lily Impeller and how it's created/growth pattern takes shape over time.

lily impeller

enter image description here

Here's a video of what I'm trying to model/animate the growth pattern of. https://youtu.be/by0JhirtO-0?t=224

I was thinking that the curves need to be extruded in the -Z direction at a 60 angle but I couldn't come up with a way of how to do this.

I'm open to other ideas or suggestions on how to do this.

See attached blend 2.83 file.

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A way to make the impeller to appear to grow like a shell is to use Boolean operations between a shape and the Lily impeller. The animation below shows an intersection between a cone and an the impeller.

enter image description here

Steps to recreate.

  1. Import/create the lily impeller.
  2. Add a cone that roughly matches the angle of the lily impeller spiral and large enough to contain the full impeller. enter image description here
  3. Animate the cone moving from the above the impeller until it fully encloses the impeller. This will generate the animation above.

The geometry for the impeller above was from https://www.thingiverse.com/thing:956458 modeled after Jay Harmans drawings, courtesy of yzorg.

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