- We’ll look at a bit (starting at 1:45 and going for a few minutes, later picking up again at 7:42) of a second video about “complex numbers” (these are the two-part numbers that involve a part from the ordinary number line and the part that is from the imaginary number line consisting of multiples of the imaginary number “i” which is the square root of -1)
- We’ll use the “Two-Variable Function Pump” to iterate the squaring function for complex numbers (as we did Monday for regular numbers). We’ll also use it to do the “two step” process of squaring and adding a number to the result.
- We’ll use a Julia Set creator to draw Julia sets for the two-step process with different values of C.
- You can also look at Julia sets pulled from the Mandelbrot set: http://www.ibiblio.org/e-notes/MSet/Anim/ManJuOrb.htm
- There are many other places to explore Mandelbrot and Julia sets:
- http://www.javaview.de/vgp/tutor/fractal/PaFractalImage.html (click in Mandelbrot set and move pointer to select different values for C and see corresponding Julia sets, can also zoom in – press “m” while selecting rectangular regions)
- http://www.ibiblio.org/e-notes/MSet/Anim/ManJuOrbB.htm (creates animations, can zoom into both Mandelbrot and Julia sets)
- http://math.bu.edu/DYSYS/applets/Quadr.html (can create animations, but resolution isn’t that good)
- http://gingerbooth.com/coursewareCBC/mandeljulia.html (can alter coloring schemes, zoom, under “Scenarios” can alter the equation used to iterate)
Your homework over the weekend is to create your own image of a Julia or Mandelbrot set using one of these tools (or another tool you find). Next week, we will start talking about symmetry, so comment on the symmetry you see (or don’t see) in your creation.