Lambda Fractal:  Additional Curves Now Seeing Them
lazarus / 39-Graphics

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Boleeman · 2024-08-07 06:41

A Lambda Fractal, producing Mandelbrot type fractal curve.

Thanks to tetrastes. Additional Curves Now Seeing Them

The Lambda formula is an alternative version of the equation for Julia
fractals. While it is capable of creating the same Julia sets, the
corresponding Mandelbrot version looks different.

Paul Bourke at https://paulbourke.net/fractals/lambda/ says "Each
value of "a" gives a different fractal image, commonly used value is
-(0.85 + 0.6 i)"

Other values:  a = 0.7 + 0.7 i       ,     a = 0.7 + 0.725 i       
 ,    a = 0.69 + 0.725 i

At  https://www.ultrafractal.com/help/index.html?/help/formulas/standa
rd/lambda.html  they also say to try:

For the standard Lambda Mandelbrot set, this should be set to (0.5,
0), which is what is shown in the attached png screenshot. Other
values create distorted shapes that can be interesting, but they are
usually not as well-formed as the standard set.
For well-formed sets, the real value should be set to 1 divided by the
real value of the exponent.
For example, use (0.25, 0) if Exponent is set to (4, 0).

Exponent:
The default value is (2, 0), resulting in the classic equation.   c *
z * (1 - z)

Try (3, 0) and (4, 0) and so on to increase the complexity of the
fractal.


I can't seem to see those other fractal curves mentioned at those 2
web sites.

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Dzandaa · 2024-08-07 17:13

Hi,

Nice Fractal (again)

B->

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tetrastes · 2024-08-08 11:51

Quote from: Boleeman on August 07, 2024, 08:41:38 amI can't seem to
see those other fractal curves mentioned at those 2 web sites.

You obviously implemented not formula from the 1st site ( zn+1 =
azn(1-zn) ).
Attached is your project modified for this formula, though with your
default settings (0.5, 0) it draws smth like ass  instead of
Mandelbrot-like. I used ucomplex unit from DMath package for
simplicity.
From the 2nd site I've understood, that this formula is special case
of more common one, but I cannot find it.

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Boleeman · 2024-08-09 07:05

tetrastes, thanks for working that out.

That explains why I could not get the other curve types.

Now getting some nice fractal curves.


Dzandaa, thanks for the nice comment.