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Welcome to Fractal Forums > Fractal Software > Help & Support > Help identifying formulas
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Author Topic: Help identifying formulas  (Read 224 times)
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tly
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Posts: 13
« on: May 12, 2016, 11:20:55 PM »
Some years ago i tested a lot of formulas and made mostly lowreslution images (because my renderer was quite bad  grin )

Now im looking at some of these images and want to rerender them with higher resolution / multisampling, but i dont remember the formulas that i used...

My question is: do you think it would be possible to identify some formulas by images? I only used the standard m-set escape time method for the fractals. Ive seen similar images before, so the formulas could be well-known  wink

these are the images that id like to rerender:




pretty weird ones:



some variation of the burning ship:

it has henon attractor shapes as "minibrots"  cheesy
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lkmitch
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Posts: 238
« Reply #1 on: May 13, 2016, 06:29:13 PM »
The first one looks like a rational function, maybe something like z = c(z^4-1)/z.

The second looks like a tweak to the regular Mandelbrot, maybe along the lines of z^2+c+(small number)/z.

No idea about the others.
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tly
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« Reply #2 on: May 14, 2016, 04:57:50 PM »
Quote from: lkmitch on May 13, 2016, 06:29:13 PM
The first one looks like a rational function, maybe something like z = c(z^4-1)/z.

The second looks like a tweak to the regular Mandelbrot, maybe along the lines of z^2+c+(small number)/z.

No idea about the others.

Thanks, i think the rational function is a good idea, this would explain why the fractal shapes get infinitely small at the origin.
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tly
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Posts: 13
« Reply #3 on: May 16, 2016, 11:00:01 PM »
I found the formula for the second image, its ((z^2 + 2*z + 0.1)/(2*z + 2))^2 + c  cheesy
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Imagyx
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Finally 3D and more... Thank you !! ;-)
« Reply #4 on: May 19, 2016, 04:31:39 PM »
Quote from: lkmitch on May 13, 2016, 06:29:13 PM
The first one looks like a rational function, maybe something like z = c(z^4-1)/z.

The second looks like a tweak to the regular Mandelbrot, maybe along the lines of z^2+c+(small number)/z.

No idea about the others.

Nice idea, I entered your formula into my little program.Result's below  smiley
Rational functions need to be tested further  grin
Thanks!

* mb0.023878724016139108pic2.png (124.49 KB, 540x374 - viewed 9 times.)
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During difficult times, keep steady and play the match.
tly
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« Reply #5 on: May 19, 2016, 09:43:03 PM »
Quote from: Imagyx on May 19, 2016, 04:31:39 PM
Nice idea, I entered your formula into my little program.Result's below  smiley
Rational functions need to be tested further  grin
Thanks!

nice smiley

what startvalue did you use for z? using z = 0 obviously doesnt work, using z = c looks different in my program...
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tly
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« Reply #6 on: May 19, 2016, 10:20:08 PM »
i tried it out a bit and found, that you used the z^3 instead of z^4 wink
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Imagyx
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Finally 3D and more... Thank you !! ;-)
« Reply #7 on: May 20, 2016, 10:16:42 AM »
Ops... I'm sorry.  embarrass
I really tried z^4 first, but it didn't look like the first one from  tly.
So I thought with functional analysis in mind to try z^3 and this one looks  more like the one which was asked for.
Well, at least there are three parts as well...I wonder why there aren't any original mandelbrots in my render but
instead some hearts  undecided

Now there's z = c(z^4-1)/z  as well:
But as always the look depends a lot on choice of colors...

* mb0.2693113583030101pic.png (45.78 KB, 646x445 - viewed 7 times.)
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During difficult times, keep steady and play the match.
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