What function has a 3D graph that will look like a spiral into a singularity?

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I am trying to draw text spiraling into a black hole, from a more interesting slightly off-orthogonal viewpoint.

I think a function that defines a black hole/singularity surface might look something like z=-1/(x^2+y^2)... but I don't know how to get from that to a set of points (locations of letters) for my text that spirals into the singularity.

Thinking out loud I would want a decreasing radius and an increasing or decreasing angle value that wraps around 2*pi (or 360) and then translates each radius,angle into an x,y,z value...

so how is this?

  • vary the radius from the largest value to the smallest value,
  • vary the angle from 0 to 2*pi*(constant-number-of-spirals)
  • vary the font size from largest value to smallest value
  • x = cos(angle)*radius
  • y = sin(angle)*radius
  • z = -1/(x^2+y^2)

Will that work? How would I get a tangent at each point to use as a baseline for each letter's "direction"? Of course I will have to translate 3D to 2D to plot the letters...