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- Newsgroups: sci.fractals
- Path: sparky!uunet!caen!zaphod.mps.ohio-state.edu!rpi!pooler
- From: pooler@vccnorthe.its.rpi.edu (Robert Peter Poole)
- Subject: Re: other iterations
- Message-ID: <9=4zj8h@rpi.edu>
- Nntp-Posting-Host: vccnorthe.its.rpi.edu
- Organization: Rensselaer Polytechnic Institute, Troy, NY
- References: <19980@ector.cs.purdue.edu>
- Date: Fri, 16 Oct 1992 19:47:36 GMT
- Lines: 31
-
-
- Well, I attended a lecture once on fractal generation... it was quite
- fascinating. Here are some variants on the mandelbrot set:
-
- z = z^n + c
-
- In this case, n determines the number of major "lobes" that the Mandelbrot-like
- set contains. For n = 2, you get a normal M-set, with a "butt" (2 lobes).
- You can also use fractional numbers for n instead of integers. I've been told
- n = 1/2 is rather boring to look at, and n = 1 is not a good idea either, but
- n = pi might be interesting, or n = 1/e.
-
- z = sin(z) + c
- z = cos(z) + c
- z = tan(z) + c
- etc.
-
- These all give fascinating repeating structures that have a Mandelbrot/Julia
- set "feel" to them. I can't really describe them too well, except to say
- that the structures tend to repeat linearly in the direction of the real
- axis (as you would expect from trig functions).
-
- Equations for complex-number equivalents of the real-number trig functions are,
- of course, available in the CRC math reference, but you can rederive them
- from the exponential equation quite easily.
-
- I am not sure how "pretty" or "interesting" the hyperbolic functions would be.
-
- Rob Poole
- pooler@rpi.edu
- pooler@cs.rpi.edu
-