Title: What is a Lambda?
Post by: Erisian on April 12, 2012, 03:33:13 PM
A Lambda looks like a double Mandelbrot but behaves like a Julia set. So which is it?
Title: Re: What is a Lambda?
Post by: Alef on April 12, 2012, 04:07:44 PM
Something based on bifurcation map or something alike. Not quite shure, but IMHO not so usefull.
Title: Re: What is a Lambda?
Post by: DarkBeam on April 12, 2012, 05:18:46 PM
A Lambda looks like a double Mandelbrot but behaves like a Julia set. So which is it?
A different formula of Mandelbrot set, invented by Benoit Mandelbrot ;)
Title: Re: What is a Lambda?
Post by: ker2x on April 12, 2012, 05:42:49 PM
http://lambda-the-ultimate.org/
http://en.wikipedia.org/wiki/Lambda_calculus
(yup, i know, it's +/- off-topic. Sorry ;D )
http://en.wikipedia.org/wiki/Lambda_calculus
(yup, i know, it's +/- off-topic. Sorry ;D )
Title: Re: What is a Lambda?
Post by: Erisian on April 12, 2012, 06:20:04 PM
A different formula of Mandelbrot set, invented by Benoit Mandelbrot ;)
For a mandelbrot, it does some amazing Julia like things.
Title: Re: What is a Lambda?
Post by: DarkBeam on April 12, 2012, 10:38:19 PM
You talk about my quaternion version? :)
Title: Re: What is a Lambda?
Post by: Erisian on April 12, 2012, 10:39:55 PM
I was talking generally. Your quat version is easier to manipulate in Julia mode.
Title: Re: What is a Lambda?
Post by: DarkBeam on April 13, 2012, 09:53:02 AM
Okay :D The only difference is the number of terms to multiply
Title: Re: What is a Lambda?
Post by: Erisian on April 13, 2012, 01:08:32 PM
I don't understand the maths, I just wondered how you would classify one.
Title: Re: What is a Lambda?
Post by: lkmitch on April 13, 2012, 05:23:03 PM
The standard lambda fractal is a Mandelbrot-type fractal (as opposed to Julia), for the equation z = lambda * z * (1 - z).
Title: Re: What is a Lambda?
Post by: Erisian on April 13, 2012, 06:17:58 PM
Dunno if I'm understanding this right but according to http://www.ultrafractal.com/help/index.html?/help/formulas/standard/lambda.html it seems to be both Mandelbrot and Julia.
Title: Re: What is a Lambda?
Post by: lkmitch on April 16, 2012, 04:52:52 PM
Dunno if I'm understanding this right but according to http://www.ultrafractal.com/help/index.html?/help/formulas/standard/lambda.html it seems to be both Mandelbrot and Julia.
No, that's just saying that Ultra Fractal has both Mandelbrot-type and Julia-type formulas for the lambda equation, z = c * z * (1 - z).
Title: Re: What is a Lambda?
Post by: Erisian on April 16, 2012, 08:34:39 PM
OK. I'm not very bright when it comes to this stuff!
Title: Re: What is a Lambda?
Post by: Adam Majewski on February 10, 2013, 05:04:24 PM
Standard function for computing Mandelbrot and Julia sets is a complex quadratic polynomial :
http://en.wikipedia.org/wiki/Complex_quadratic_polynomial (http://en.wikipedia.org/wiki/Complex_quadratic_polynomial)
 = z^2 + c)
One can use other formula :
 = \lambda *z*(1 - z))
It can be used for drawing :
* one parameter plane ( lambda plane ) where is Mandelbrot set. Here z0 is a critical value.
* many dynamic planes ( z planes ) where are Julia sets. Here lambda is a constant value.
See also :
http://en.wikibooks.org/wiki/Fractals/Iterations_in_the_complex_plane/qpolynomials (http://en.wikibooks.org/wiki/Fractals/Iterations_in_the_complex_plane/qpolynomials)
HTH
Adam
http://en.wikipedia.org/wiki/Complex_quadratic_polynomial (http://en.wikipedia.org/wiki/Complex_quadratic_polynomial)
One can use other formula :
It can be used for drawing :
* one parameter plane ( lambda plane ) where is Mandelbrot set. Here z0 is a critical value.
* many dynamic planes ( z planes ) where are Julia sets. Here lambda is a constant value.
See also :
http://en.wikibooks.org/wiki/Fractals/Iterations_in_the_complex_plane/qpolynomials (http://en.wikibooks.org/wiki/Fractals/Iterations_in_the_complex_plane/qpolynomials)
HTH
Adam