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Fwiw here is an experimental tiling I am playing around with. Seems pretty interesting. Have you seen it before?

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#Fractal #Tile #Math #Art #Space #Tile
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Fwiw, here is a Julia field fractal of mine using some coarser settings. The field gets bigger and starts creating trees with large trunks.

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#Fractal #Math #Julia #Space #Vector #Field #Art
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Here is my crappy first try at +Roger Bagula 's cubic:

It has the basic internal shapes, but not the beauty. He is using a different color monitor algorithm! Humm... Need to play around with this!

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#Fractal #Julia #Math #Art
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A power of 4 IFS Julia at point:

.575 + .06 * I

With the following weights:
______________________________
if (r < .9)
{
z = // root 0
}

else if (r < .95)
{
z = // root 1
}

else if (r < .98)
{
z = // root 2
}

else
{
z = // root 3
}
______________________________

The weights are getting harder and harder to find as the power increases!

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#Fractal #IFS #Julia #Art #Math
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I GOT IT!!!!! Doing a little dance... Finally! I thought it would be damn near impossible. Well, I guess the lesson is: NEVER GIVE UP!

Wow. Here is the formula:

z = pow(z, 3) - (pow(-z, 2.00001) - 1.0008875);

I am VERY happy! I just needed to calm the heck down and: Think. I guess another lesson is, try not to work when you are nervous. Damn it!

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#Fractal #Julia #Cubic #Art #Math
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A 64-ary dense field plot of the Mandelbrot set z=z^2+c.

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#Fractal #Math #Mandelbrot #Space #Art #Vector #Field
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Here is another compilation wrt playing around with the z-axis by simply twisting it a bit. Some interesting formations arise.

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#Fractal #3d #Math #Art #Space #Vector #Flow #Trigonometry
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A power of 3 inverse iteration Julia at point:

-.5 + .06 * I

With the following weights for the three roots:
______________________________
if (r < .0333333333333)
{
z = // root 0
}

else if (r < .766666666666)
{
z = // root 1
}

else
{
z = // root 2
}
______________________________

Fairly decent detail in the spirals...

;^)

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#Fractal #Julia #Art #Math
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My cubic Julia in Xaos. So far, I have it working fine in several of my C and C++ programs, along with Xaos. I need to get it to work in Ultra Fractal damn it! I am a newbie in that program. Fwiw, the formula from that works in Xaos is:

Z^3 - ((-Z)^2.00001 - 1.0008875)

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#Fractal #Cubic #Julia #Math #Art
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Simply adding a single iteration of:

z = pow(z, -4) - .25;

before:

z = pow(z, 3) - (pow(-z, 2.00001) - 1.0008875);

Give this most interesting fractal.

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