Phoenix Bulb

cKleinhuis

Administrator
Fractal Senior

Posts: 7044

formerly known as 'Trifox'

Phoenix Bulb

« on: December 17, 2009, 10:05:27 PM »

the phoenix fractal rendered with triplex algebra:

$z_{n+1}=z^2+cz_{n-1}$

the images below are:

1. exponent = 8 phoenix triplex fractal
2. exponent = 2 phoenix triplex fractal ( the one you could resemble when compared to
3. a julia variation ( extremely interesting behaviour )
4. the classic 2d version, rendered with ultrafractal from fractint formulas

phoenix_bulb_8.png (873.64 KB, 1023x753 - viewed 294 times.) phoenix_bulb_2.png (475.02 KB, 640x686 - viewed 301 times.) phoenix_julia2.png (317.67 KB, 640x686 - viewed 305 times.) phoenix_2d.png (128.48 KB, 640x480 - viewed 285 times.)
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divide and conquer - iterate and rule - chaos is No random!

BradC

Safarist

Posts: 85

Re: Phoenix Bulb

« Reply #1 on: December 17, 2009, 10:34:42 PM »

Wow, what does the back of that Julia set look like?


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cKleinhuis

Administrator
Fractal Senior

Posts: 7044

formerly known as 'Trifox'

Re: Phoenix Bulb

« Reply #2 on: December 17, 2009, 10:53:14 PM »

it looks from every view different wink

but i have found some very friendly looking fractal faces, one was lost ( gpu breakdown ) but i will post as soon as i have more

it is amazing to view the effect of the 3d triplex parameters, it seems so intuitive ...

i will ask subblue if i am allowed to publish a modified version of his script

next step will be:

add full alternation capabilities ( alternate formula + alternate seeds ) , this will be fun^10, but parameter wars !!!


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divide and conquer - iterate and rule - chaos is No random!

BradC

Safarist

Posts: 85

Re: Phoenix Bulb

« Reply #3 on: December 18, 2009, 06:15:19 AM »

I like this one, and I'm trying to implement it. How did you begin the iteration for the Mandelbrot set? To calculate the first z₁, I need to know both z₀ and z_-1. I can't use z₀=z_-1=0 because then z₁=0, z₂=0, etc.. To begin the Julia set, did you use z₀=z_-1?


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cKleinhuis

Administrator
Fractal Senior

Posts: 7044

formerly known as 'Trifox'

Re: Phoenix Bulb

« Reply #4 on: December 18, 2009, 02:24:37 PM »

z0 is the pixel, or the 3d coordinate you want to calculate the iteration value for


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divide and conquer - iterate and rule - chaos is No random!

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it was a great time but no longer maintainable by c.Kleinhuis contact him for any data retrieval, thanks and see you perhaps in 10 years again

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it was a great time but no longer maintainable by c.Kleinhuis contact him for any data retrieval,
thanks and see you perhaps in 10 years again