# Trying to animate an extrude in 3D using curves generated by an equation over time

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:

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

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.