Lacunarity

[pucicu]

Does anyone has experience in applying lacunarity on time series or even in 2D images and how to interpret the results?

[Jules Ruis]

Please explain what is Lacunarity.

[heneganj]

No I didn't know either.

http://www-swiss.ai.mit.edu/~rauch/lacunarity/lacunarity.html

[Jules Ruis]

So Lacunity has to do with the 'holes' in the fractal.

Mathematically it means that on hole-places the value of the fractal is going to infinity i.s.o. to zero.

It is possible to fill these 'holes' with different  fractal colors. If you are interested in it how to to this, I can tell you.

[matera]

I learned early on that "lacuna" means "for the next ten minutes your computer is going to be calculating a whole lot of nothing interesting" LOL

[alan2here]

so like the inside part (often rendered as black) in the middle of the mandlbrot set?

[David Makin]

"Lacunarity" is usually used in association with IFS or Strange Attractors rather than escape-time fractals. It's an extra way of characterising them in addition to fractal dimension.

[Adamsliu]

Could u tell me how to caculate lacunarity,are there any useful software?

[Nahee_Enterprises]

Adamsliu wrote:
>
>    Could u tell me how to caculate lacunarity,
>    are there any useful software?

There are several web pages that give such information, a quick search using Google on the word "lacunarity" will show about 45,600 pages.  A good start would be this one:  http://local.wasp.uwa.edu.au/~pbourke/fractals/lacunarity/

[Charleswehner]

That diagram is very reminiscent of the Hamming codes (binary that changes only one bit at a time as it progresses). However, it is definitely not the same.

Charles

[Charleswehner]

That diagram is very reminiscent of the Hamming codes (binary that changes only one bit at a time as it progresses).

I said that wrong. What I meant was the Gray Code. However, the Hamming Codes (self-correcting codes) also produce banded images like that above.

If "Lacunarity" decreases with density, then the regions of the attractors must have high lacunarity when in the region of the attractors, in the inner set, and low lacunarity in the same regions of the outer set.

Here I have arranged for an outer set and inner set fractal to alternate. The outer set has tiny black dots containing the entire Mandelbrot set, therefore dense and of small lacunarity. The inner set has circles, which meet the definition of "coarse", and therefore of high lacunarity.

One wonders whether the introduction of the term "strange attractors" is a red herring. Surely, this applies generally to all patterns - with or without attractors.

Charles