Talk:Lévy C curve

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Image size

There is a lot of detail in the images that can't be seen on my screen at the current size. I think they should be larger. Any suggestions or objections as to how large? Hyacinth 10:30, 29 September 2006 (UTC)[reply]

Duh! A larger image would show just the same fine detail, only more of it. It's a fractal, you know.
—Herbee 23:57, 27 October 2006 (UTC)[reply]

The image does not feature an infinite number of iterations, duh. We wouldn't be "zooming in" to further levels, we would just be making the levels we already have more visible. Hyacinth 07:35, 28 October 2006 (UTC)[reply]

evolution

it would be helpful to see the evolution of the curve; perhaps each iteration in a different colour.JK-Salisbury 86.160.138.236 (talk) 10:50, 3 June 2008 (UTC)[reply]

Done - articles now has diagram showing first 8 stages of curve construction. Gandalf61 (talk) 12:33, 3 June 2008 (UTC)[reply]

Not a fractal is misleading

It doesn't make sense to insist that the C curve is not a fractal simply because its Hausdorff dimension is 2. This figure has all the other features of fractals -- self-similarity, detailed structure at arbitrarily small scales, irregularity not easily described with Euclidean geometry, a simple definition. To say that it's not a fractal just because its area happens to scale up at the same rate as an ordinary figure on a plane is a little ridiculous.

It's like saying 2 isn't a fraction. I suppose you could say that in some sense, but if you gave a rigorous definition of fractions, you'd probably get something like the rational numbers, which obviously include 2. The collection of numbers that are rational but not integers is, mathematically speaking, not a particularly interesting or useful set as far as I can tell. Likewise, I see no utility in ejecting a subset of figures from the class of "fractals" simply because they happen to have integral Hausdorff dimensions.

To put it another way, the set of rational numbers is in some sense the set of all numbers that can be constructed by pairing integers in ratios. 2 is in that set -- the fact that it is also in the set of integers is irrelevant. In the same way, the C curve is a cure that is constructed in the way fractals are constructed -- the fact that the result has some of the same properties as a simple plane figure is irrelevant.

Pushed to its extreme, this is an argument for including plane figures like squares in the class of fractals because they too can be constructed in a fractal-like way. The history section of the fractal page hints at this way of thinking. I think this is a much better way to think about fractals -- plane figures are in the set of things that can be constructed by "ordinary means", but they are also in the set of things that can be constructed in the manner of fractals.

If you disagree, fair enough. But in that case, I have to insist that your definition of "fractal" is fuzzy, and so putting not a fractal in bold is misleading, because by a fuzzy definition, nothing is not a fractal with 100% certainty.

I'll add that -- for people who care about sources -- in the very same sentence there is a link to Wolfram MathWorld calling the C curve a fractal. The title of the page is "Levy Fractal.". Solemnavalanche (talk) 13:12, 20 November 2015 (UTC)[reply]