I’ve decided today that my next project will be to create a basket case fractal. I have a picture in my mind of a gift basket type thingy, but I can’t decide what to put into it.
I’ll be working with an iteration of z = z^2 + c with a view then to producing a gift basket of the Mandelbrot kind.
The initial z word will be zero, for no other reason than it seems to be a fitting place to start. Thus giving
zero = zero squared + c
as my first iteration of the basket case fractal.
c is the point of my indecision. It’s complex, which suggests that it is partly real and partly imaginary.
Real numbers can be represented on a one dimensional line called the real number line.
and
Since complex numbers have two parts, a real one and an imaginary one, we need a second dimension to graph them. We simply add a vertical dimension to the real number line for the imaginary part.
Ok. That makes perfect sense.
However, I’m not looking to put a complex number into my gift basket. I’m looking for a highly distinctive selection.
If it was up to me I’d go for a selection of biscuits and cheese, but I’m not doing this for myself. Let me reiterate – I want this to be a gift basket fractal, so submissions for c are now open.
July 1st, 2011 at 6:55 am
Well, I’m a real fan of 9.
it’s odd but has the harmony of being 3 3′s
A trinity of trinities. Nine sides make a nonagon
(which sounds like the kind of form one could toss off as if it were nothing)
the number on the threshold of tripping into the binary.
It could be nicely divided amongst friends in telling ways:
One for you and two for me
Two for you and one for me
One for you, one for me,
one to leave
for the mystery guest.
July 5th, 2011 at 5:08 pm
It’s amazing what that 9 revealed when i plugged it into the complex plane. Of course I had to convert it from an absolute nine into a complex representation first, then weed out the obvious cliches (not that the resulting cliches were without value – I rediscovered Robert Burns at one point!) Looking forward to experimenting more with it. Thanks Bonnie!
July 1st, 2011 at 11:08 am
i like bonnie’s nine. back at fractal central i will have to try that 0 thing as i am not exactly clear on zero as an integer, since any other everyday math proposes 0+0 or 0-0
or 0×0 is 0. so there might not an iteration to generate, it would make the “black hole” space instead. the space around the iterations so to speak spatially where most iterations are viewed 2D, so there’d have to be an abstract perspective for viewing the depth lets say of the space around the iterations. and 0 would work perfectly well for that, it would seem, but how does a 0 jumpstart an iteration?
July 5th, 2011 at 5:18 pm
This turns out to be very fascinating indeed Kathi. Fractal central I assume is at (0,0i), and to take that as a ‘c’ should produce something like a black hole singularity, since as you say, it can’t generate an iteration.. Thing is, when I tried it myself, I found a result. It made me feel sad though, and I’m not sure I want to show anyone what I found. Thank you Kathi.
July 7th, 2011 at 4:31 am
i went back to the online generator and also got some results tho they were unusual in spatial composition as shown in the frame of the generator. however, i had to override presets which i was only allowed to do using julia so the mandelbrot result was not exactly 0 based, but the julia result was ‘almost’ all black space but for some feathers in one corner
July 1st, 2011 at 10:48 pm
and the card attached to the basket reads “you’ve been gleicked!”
July 5th, 2011 at 5:25 pm
Thanks Mark :) I can see an opportunity to print a series of ‘iGleick U’ cards, but I fear there may be more than one legal barrier standing in the way. I’ve read though that mathematical results can’t be held to copyright law, so maybe there’s a way around it?
July 5th, 2011 at 11:02 pm
funny you say that about math and copyright law. when i read gleick’s book years ago, i was left with the distinct impression of “so what”. i never got what was so special about complex numbers, it was just plain old math to me.