spiraMira.gif

Spira Mirabilis
the miraculous logarithmic spiral

A logarithmic spiral can be defined parametrically as such:

where \(a\) and \(b\) are constants. In the above gif, \(a = 0.3\) and \(b = 0.1759\).

logLine.gif

A logarithmic spiral can also be made by connecting a point on ray to a neighboring ray by a perpendicular. Repeating this for many equally spaced rays will result in a logarithmic spiral, increasingly smooth the more rays are used.

It occurs to me only after completing it that not all of the rays on the above image are, in fact, equally spaced. This may add a bit of funniness to the spiral, but shouldn't make too much of a difference since it all gets smoothed out in the limit anyways. The above image was also drawn and not generated so some of the lines that ought to be perpendicular aren't, exactly.

Code: Download spiraMira.zip