If you aren’t familiar with logarithmic spirals, you’ll likely still recognize the form. It’s found throughout the natural world at vastly different scales. The same shape can be seen in sea shells and also universes which is seriously profound if you ask me. You can read all about this type of spiral including the geeky math bits here… http://en.wikipedia.org/wiki/Logarithmic_spiral
Now for the 3D modeling trick! You can draw a logarithmic spiral using a radial array of lines and the ability to snap to perpendicular intersections. I used Rhino which has some handy Osnaps to make this extra easy.
It’s important to draw an interpolated curve so that the control points you place pass through the perpendicular intersections. Just continue to snap to the next 90° intersection making your way around the array of lines as you spiral inward.
Using a vector based program is best for this so that you can continue to zoom infinitely in as you go. The resulting curve can be used for anything you like and will have a natural symmetry that is… um… universal.