These are my all new, brand spankling Julia curves. Fresh off the good old DD floppies this Easter!!
They are created using the very same formula except that this time instead of plotting the values of c. You plot the different starting values for a fixed c. If that particular c is in the Mandelbrot set then the point (0,0) will be contained on the Julia curve. But the most interesting examples of Julia curves are when you use a value or c which is near the edge or just outside the Mandelbrot set.
Julia curves
These three pics are all of the same Julia curve, with c=-1.1-0.15i. The first covers the region -2 to 2 along both the real and imaginary axes. The second has it's left edge at -0.33, it's right edge at -0.18, it's top edge at 0.4i and it's bottom edge at 0.25i. The third has it's left edge at -0.25, it's right edge at -0.23, it's top edge at 0.29i and it's bottom edge at 0.27i.
The Three pictures are zooming closer and closer into the curve. Note that the features on the edge repeat themselves at many diffenert scales. It has been conjectured (I don't think anyonw has proven it yet!) that this will continue indefinately at closer and closer magnifications. This is a common feature of fractals and one of the things that makes them so interesting.
This is the julia curve with c=-.7i. It's left edge is at -0.8, it's right edge at 0.5 it's top edge at 1.2i and it's bottom edge at -0.1i
Above: c=-0.68-0.35i
The pic on the left took 38 minutes to render.
Both of these pics are Julia curves with c=-0.73+0.113i. The second is a close up of the region -0.2 to 0.3 horizontally and 0.3i to 0.9i vertically.
