greentexas


« on: November 06, 2016, 02:00:33 PM » 

Hello, I'm wondering whether anyone has any experience zooming into unfamiliar powers of the Simonbrot.
I know the formula for the Simonbrot 4th as z^{2} * z^{2} + pixel.
The formula for the 6th Simonbrot is z^{3} * z^{2} + pixel.
Does anybody have experience zooming into fractals like z * z^{2} + pixel (Quadratic Simonbrot) or z^{4} * z^{2} + pixel? (8th Simonbrot?)
If so, notify me.



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greentexas


« Reply #2 on: November 06, 2016, 07:46:34 PM » 

You are correct. There is a fourth and sixth power Simonbrot in Kalles Fraktaler. But I'm not aware of any 2nd degree Simonbrot in Kalles Fraktaler.



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TheRedshiftRider


« Reply #3 on: November 06, 2016, 08:01:49 PM » 

You are correct. There is a fourth and sixth power Simonbrot in Kalles Fraktaler. But I'm not aware of any 2nd degree Simonbrot in Kalles Fraktaler.
I must have read your post incorrectly. At this point those variants are not implemented at this point. Would indeed be cool to see them implemented.



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greentexas


« Reply #4 on: November 06, 2016, 10:47:00 PM » 

It would also be nice to see Simonbrot 3rd, 5th, and 7th, but the formulas for these fractals are z^{1.5} * z^{2} + pixel, z^{2.5} * z^{2} + pixel, and z^{3.5} * z^{2} + pixel.
Due to the fact that the powers of some of the terms are fractions, this could be difficult to implement. In a roundabout way, there is a power zero Simonbrot on Kalles Fraktaler, because the power zero Simonbrot is actually the Burning Ship.



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simon.snake
Fractal Bachius
Posts: 640
Experienced Fractal eXtreme plugin crasher!


« Reply #5 on: November 07, 2016, 10:37:46 PM » 

I have to say I find it really weird (in a nice way) that there is all this talk of the simonbrot.
It is a little surreal to have people discussing something I found.
It may well have been found before I discovered it  there were thousands of formulas created for the formula parser in FractInt.
Anyway, do not stop talking about it just because I find it weird. There probably are a whole load of different variants of the base formula still waiting to be discovered.



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greentexas


« Reply #6 on: November 08, 2016, 12:48:02 AM » 

I actually found the Simonbrot strange when I first saw it (when it was added to Kalles Fraktaler). I have no evidence of anybody seeing it before that time.
Also, I would think of this formula creating something of a Simonbuffalo:
z^{2} * z^{2} + pixel
because the formula for the Buffalo is z^{2} + pixel.



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simon.snake
Fractal Bachius
Posts: 640
Experienced Fractal eXtreme plugin crasher!


« Reply #7 on: November 08, 2016, 02:26:08 PM » 

I was playing in FractInt last night and found that (in FractInt formula parser syntax):
z = abs(z) * z + c followed by z = z * z + c
(so only slightly different from the base formula by way of a +c on the first line)
Produces another similar fractal but with mandelbrot style minibrots when zoomed in.
I don't know how you'd code that into your convention.
Strange.



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greentexas


« Reply #8 on: November 08, 2016, 11:59:30 PM » 

The formula for that fractal, as far as I can tell, is: z^{2} * z + c. In z power, this formula appears to be something of a hybrid between the Mandelbrot and the Simonbrot.
In a roundabout way, this is the Mandelbrot formula:
z^{2} * z^{0} + c.
(z^{0} is always 1, and don't forget the identity property of multiplication!)
The Simonbrot has z power two, and your new fractal has z power one.



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LionHeart


« Reply #9 on: April 17, 2017, 02:47:02 AM » 

Hi, I'm trying to implement the entire suite of SimonBrot fractals. I have success with the even functions: int DoSimonSnakeFormula(void) { Complex zabs, tempz; zabs.x = fabs(z.x); zabs.y = fabs(z.y); tempz.y = z.y * zabs.x + z.x * zabs.y; tempz.x = z.x * zabs.x  z.y * zabs.y; z = tempz; z = CPolynomial(z, degree) + pixel; return (CSumSqr(z) >= rqlim); } I would like to upgrade my complex arithmetic routines to include fractional powers of complex numbers. Has anyone else been able to make progress here? Thanks to all who contributed



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Paul the LionHeart



LionHeart


« Reply #10 on: April 17, 2017, 02:20:45 PM » 

Hi Guys, I have built a square root function into my complex library and seem to have some success with Simon Brot. I have nothing to test against, so I don't know if I have a bug int DoSimonSnakeFormula(void) { Complex zabs, tempz, sqrtz; zabs.x = fabs(z.x); zabs.y = fabs(z.y); tempz.y = z.y * zabs.x + z.x * zabs.y; tempz.x = z.x * zabs.x  z.y * zabs.y; sqrtz = (degree % 2 == 1) ? CSqrt(z) : 1.0; // use square root power if degree is odd z = CPolynomial(tempz, degree / 2)* sqrtz + q; return (CSumSqr(z) >= rqlim); } Please let me know if there are any images for Simonbrot 3rd, 5th, and 7th, using the formulas for these fractals: z1.5 * z2 + pixel, z2.5 * z2 + pixel, and z3.5 * z2 + pixel Thanks



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Paul the LionHeart



simon.snake
Fractal Bachius
Posts: 640
Experienced Fractal eXtreme plugin crasher!


« Reply #11 on: April 17, 2017, 08:57:08 PM » 

Any pictures yet? I'd love to see what the initial render at standard coordinates looks like.



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LionHeart


« Reply #12 on: April 18, 2017, 04:52:24 AM » 

Hi Simon, Here are the 8 SimonBrot images I produced so far using the algorithm in my previous post. Simonbrot 2nd, 3rd, 4th, 5th, 6th, 7th, 8th and 9th: The formulas for these fractals are: z^1.0 * z^2 + pixel, z^1.5 * z^2 + pixel, z^2.0 * z^2 + pixel, z^2.5 * z^2 + pixel, z^3.0 * z^2 + pixel, z^3.5 * z^2 + pixel, z^4.0 * z^2 + pixel, z^4.5 * z^2 + pixel. Can you verify the fractional ones? Many thanks Paul the LionHeart



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Paul the LionHeart



simon.snake
Fractal Bachius
Posts: 640
Experienced Fractal eXtreme plugin crasher!


« Reply #13 on: April 18, 2017, 11:26:06 PM » 

I'm not sure how I can verify anything. I made up the SimonBrot but I haven't played extensively with the formula to create other powers. When the formula was being converted to something usable in Fractal eXtreme there were other variants made. I don't think they looked much like what you have here though. I'll try to dig out a picture of the different types, if I still have it on my Laptop. Had a quick look but no joy so far. Will continue looking. Meanwhile, here's a formula for one I call Kung Fu Panda: kungfupanda { ; burning ship variant ; SMF abs(z*z) in place of abs(z). if (ismand) p = 0pixel z = p else p = 0p1 z = 0pixel endif: z = abs(z*z) z = z * z + p z < 4 }



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To anyone viewing my posts and finding missing/broken links to a website called www.needanother.co.uk, I still own the domain but recently cancelled my server (saving £30/month) so even though the domain address exists, it points nowhere. I hope to one day sort something out but for now  sorry!



LionHeart


« Reply #14 on: April 18, 2017, 11:33:24 PM » 

Hi Simon, Using the ManpWIN fractal interpreter, I got: z=c=pixel z = abs(z*z) *abs(z*z) + c Does it look right?



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Paul the LionHeart



