• January 28, 2022, 11:57:41 AM

### Author Topic:  My variations on the Spider. Are new or are already invented?  (Read 224 times)

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#### julofi

• Fractal Furball
• Posts: 295
##### My variations on the Spider. Are new or are already invented?
« on: January 12, 2022, 07:33:34 PM »
Hi, playing with the formula designer I got two variations of the spider formula. I called Conjugated Spider A and Conjugated Spider B.

Conjugated Spider A
The original Spider formula is Z= Z^2 + C : C= C/2 + Z;  with Z = C in previous operations.
My version is Z= Z^2 + conjugate(C) : C= C/2 + Z;  with Z = C in previous operations. Of course, I generalize using any complex exponent instead of 2.
The default view, with exponent 2, default palette, is quite simple. Just look at the attached Spider-Conjugated A default pic.
However, just rotating the image 90º and applying another palette with colouration by distance to supershape I get the image Spiky Uterus.
It reveals to be quite less simple when using negative exponents. See examples
Brown image is just a general view of the fractal, no zoom, with exponent -3
Green image is another general view of the fractal, without zoom, with exponent -4,0.5i
Another example I posted in DeviantArt, with exponent -2, 0.5i
https://www.deviantart.com/jlfractals/art/JLF3298-Wingspan-902693811

[Continues in next post]

#### julofi

• Fractal Furball
• Posts: 295
##### Re: My variations on the Spider. Are new or are already invented?
« Reply #1 on: January 12, 2022, 07:42:05 PM »
My second variation of the Spider formula:
Conjugated Spider B
It is just like the Spider formula but changing the previous operations, before the iteration loop. Instead of Z = C, I use Z = Conjugate(C)
So the formula of my variation is:
Z = conjugate(C) (in previous)
Z = Pow(Z, E) + C
C = C / 2 + Z

The fractal looks more alike the spider formula. Curiously negative exponents are quite simple, but complex exponents with the real part positive are quite rich.
In the image, the fractal with default exponent 2, colouration by default.

So, my question is, are my Conjugated Spider variations already invented? Or are they new?

#### Alef

• Fractal Frogurt
• Posts: 496
• a catalisator / z=z*sinh(z)-c^2
##### Re: My variations on the Spider. Are new or are already invented?
« Reply #2 on: January 12, 2022, 10:42:07 PM »
There are formulas with optional changable functions. I don't know all the formulas, but Z = F1(C) could be in certain realisation of spider with F1 being changable function.

...
Fractal Explorer had something like (original description):
Z=C°=Z°: Z=Z*Z+Fn1(C)+Julie; C=C/2+Fn2(Z)"
With F1 and F2 being changable functions including conjugate, generating fractal like the 1st picture. This is just a conj(x,y)=(x,-y) Too mutch formulas could make it more hard to comprehend it. But uterus fractal formula is fun to have;)
« Last Edit: January 12, 2022, 11:00:33 PM by Alef »
by Edgar Malinovsky aka Edgars Malinovskis.

#### julofi

• Fractal Furball
• Posts: 295
##### Re: My variations on the Spider. Are new or are already invented?
« Reply #3 on: January 12, 2022, 11:31:36 PM »
I have checked Fractal Explorer. It includes tons of functions to each formula.
I applied a Conjugate function to Spider and I found something similar, but not the same. Not the first one, not the second one.
Here, an image.
This is the Spider formula in Fractal Explorer: Z=C°=Z°: Z=Z*Z+Fn1(C)+Julie; C=C/2+Fn2(Z)"
So choosing Conjugate for first function and Ident for second one, it would be something like Z=Z^2 + Conjugate(C) + Julie : C=C/2 + Z
I don't know what that Julie is, but I have just tried other functions, without this "Julie" in FFExplorer and none of them are the same. So, there must be something else.
In fact his Spider formula without extra functions (that is using Ident for both optional functions) looks quite different.
« Last Edit: January 12, 2022, 11:46:00 PM by julofi »

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