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 298 times.) phoenix_bulb_2.png (475.02 KB, 640x686 - viewed 304 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

The All New FractalForums is now in Public Beta Testing! Visit FractalForums.org and check it out!

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