Logo by S Nelson - Contribute your own Logo!

END OF AN ERA, FRACTALFORUMS.COM IS CONTINUED ON FRACTALFORUMS.ORG

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

this forum will stay online for reference
News: Did you know ? you can use LaTex inside Postings on fractalforums.com!
 
Home Help Search Gallery Downloads Login Register
*
Welcome, Guest. Please login or register. November 29, 2025, 07:19:57 PM


Login with username, password and session length


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


Welcome to Fractal Forums > Fractal Art > Images Showcase (Rate My Fractal) > Pandemonium #1
Pages: [1]   Go Down
« previous next »
  Print  
Share this topic on DiggShare this topic on FacebookShare this topic on GoogleShare this topic on RedditShare this topic on StumbleUponShare this topic on Twitter
Author Topic: Pandemonium #1  (Read 892 times)
0 Members and 1 Guest are viewing this topic.
Fractal Ken
Fractal Lover
**
Posts: 246


Proud to be 2D
« on: May 23, 2011, 09:01:06 PM »


Generated by homemade software with minor post-processing in GIMP.
Logged
Fortran will rise again
Pauldelbrot
Fractal Senior
******
Posts: 2592



pderbyshire2
« Reply #1 on: May 24, 2011, 08:01:14 AM »
What was generated by homemade software? All I see in your post is that line of text, and the signature below it. No image (nor a broken-image placeholder).
Logged
My fractal videos.
Fractal Ken
Fractal Lover
**
Posts: 246


Proud to be 2D
« Reply #2 on: May 24, 2011, 09:37:57 AM »
Quote from: Pauldelbrot on May 24, 2011, 08:01:14 AM
What was generated by homemade software? All I see in your post is that line of text, and the signature below it. No image (nor a broken-image placeholder).

How strange! The fractal appears for me in two different browsers, and I'm sure I didn't already have it cached. Hopefully, its invisibility was a temporary glitch.
Logged
Fortran will rise again
Pauldelbrot
Fractal Senior
******
Posts: 2592



pderbyshire2
« Reply #3 on: May 25, 2011, 07:37:52 AM »
It seems to have been. It's there now, and fairly nifty. Real/real system?
Logged
My fractal videos.
Fractal Ken
Fractal Lover
**
Posts: 246


Proud to be 2D
« Reply #4 on: May 25, 2011, 05:14:44 PM »
Quote from: Pauldelbrot on May 25, 2011, 07:37:52 AM
It seems to have been. It's there now, and fairly nifty. Real/real system?

Thanks! I'm afraid I don't understand the term "real/real system," but I'll try to describe how this Julia set was generated.

Iteration formula . . .
Let z(-1) = z(0) = standardized pixel coordinates, often called "c"
For n = 1 to 100
   Define s, t, u, and v by: z(n - 1) = complex(s, t) and z(n - 2) = complex(u, v)
   Let z(n) = complex(s*u - t*v + 0.4, 2*s*t + 0.1)

Zoom region . . .
Real axis: -0.0225 to 0.1224
Imaginary axis: 0.89 to 0.99

No points escape. I used the imaginary axis as an orbit trap for the inside coloring.
Logged
Fortran will rise again
Pauldelbrot
Fractal Senior
******
Posts: 2592



pderbyshire2
« Reply #5 on: May 26, 2011, 08:22:49 AM »
Hrm. That's almost a normal Julia set iteration, except that you're using the last two points -- and then, almost a normal complex multiplication of those points, except the "imaginary" part of the result is calculated more like that of a square ...

Since it's not an analytic map of the complex plane, even if you're using something (UF?) that treats all iteration points as complex, it's really a system of two real variables x and y involving not only xn-1 and yn-1 but also xn-2  and yn-2. Indeed, the simplest expression as a straightforward iteration involves four real variables:

xn = xn-1zn-1 - yn-1wn-1 + 0.4;

yn = 2xn-1yn-1 + 0.1;

zn = xn-1;

wn = yn-1.
Logged
My fractal videos.
Fractal Ken
Fractal Lover
**
Posts: 246


Proud to be 2D
« Reply #6 on: May 26, 2011, 06:52:55 PM »
Quote from: Pauldelbrot on May 26, 2011, 08:22:49 AM
Since it's not an analytic map of the complex plane, even if you're using something (UF?) that treats all iteration points as complex, it's really a system of two real variables x and y involving not only xn-1 and yn-1 but also xn-2  and yn-2. Indeed, the simplest expression as a straightforward iteration involves four real variables:

xn = xn-1zn-1 - yn-1wn-1 + 0.4;

yn = 2xn-1yn-1 + 0.1;

zn = xn-1;

wn = yn-1.

I'm not using UF, just my own software. It does indeed treat all iteration points as complex.

I like your approach using four real variables. I'd never thought of the iteration formula that way.
Logged
Fortran will rise again
Pauldelbrot
Fractal Senior
******
Posts: 2592



pderbyshire2
« Reply #7 on: May 27, 2011, 08:48:04 AM »
Thanks. smiley
Logged
My fractal videos.
Pages: [1]   Go Down
« previous next »
  Print  
« previous next »
 
Jump to:  


Powered by MySQL Powered by PHP Powered by SMF 1.1.21 | SMF © 2015, Simple Machines

Valid XHTML 1.0! Valid CSS! Dilber MC Theme by HarzeM
Page created in 0.379 seconds with 26 queries. (Pretty URLs adds 0.007s, 2q)