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Welcome to Fractal Forums > Fractal Math, Chaos Theory & Research > Mandelbrot & Julia Set > What is a Lambda?
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Author Topic: What is a Lambda?  (Read 4829 times)
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Erisian
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« 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?
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Alef
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« Reply #1 on: April 12, 2012, 04:07:44 PM »
Something based on bifurcation map or something alike. Not quite shure, but IMHO not so usefull.
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DarkBeam
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« Reply #2 on: April 12, 2012, 05:18:46 PM »
Quote from: 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?

A different formula of Mandelbrot set, invented by Benoit Mandelbrot wink
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ker2x
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« Reply #3 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  grin )
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often times... there are other approaches which are kinda crappy until you put them in the context of parallel machines
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Erisian
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« Reply #4 on: April 12, 2012, 06:20:04 PM »
Quote from: DarkBeam on April 12, 2012, 05:18:46 PM
A different formula of Mandelbrot set, invented by Benoit Mandelbrot wink

For a mandelbrot, it does some amazing Julia like things.
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DarkBeam
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Fragments of the fractal -like the tip of it
« Reply #5 on: April 12, 2012, 10:38:19 PM »
You talk about my quaternion version? smiley
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Erisian
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« Reply #6 on: April 12, 2012, 10:39:55 PM »
I was talking generally.  Your quat version is easier to manipulate in Julia mode.
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DarkBeam
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Fragments of the fractal -like the tip of it
« Reply #7 on: April 13, 2012, 09:53:02 AM »
Okay cheesy The only difference is the number of terms to multiply
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Erisian
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« Reply #8 on: April 13, 2012, 01:08:32 PM »
I don't understand the maths, I just wondered how you would classify one.
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lkmitch
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« Reply #9 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).
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Erisian
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« Reply #10 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.
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lkmitch
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« Reply #11 on: April 16, 2012, 04:52:52 PM »
Quote from: 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.

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).
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Erisian
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« Reply #12 on: April 16, 2012, 08:34:39 PM »
OK.  I'm not very bright when it comes to this stuff!
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Adam Majewski
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« Reply #13 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

f_c(z) = z^2 + c


One can use other formula :

f_m(z) = \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

HTH

Adam
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