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Mandelbrot Zooms Now Surpass the Scale of the Observable Universe
StartsWithABang writes You're used to real numbers: that is, numbers that can be expressed as a decimal, even if it's an arbitrarily long, non-repeating decimal. There are also complex numbers, which are numbers that have a real part and also an imaginary part. The imaginary part is just like the real part, but is also multiplied by i, or the square root of -1. It's a simple definition: the Mandelbrot set consists of every possible complex number, n, where the sequence n, n^2 + n, (n^2 + n)^2 + n, etc.—where each new term is the prior term, squared, plus n—does not go to either positive or negative infinity. The scale of zoom visualizations now goes well past the limits of the observable Universe, with no signs of loss of complexity at all.
Technically the description of the Mandlebrot set is encoded within the observable universe so there is a problem in recursion her.
Second how is this surprising to anyone ? It's long been possible to describe and mathematically manipulate sets with more elements than the observable universe.
A zoom into a fractal stored as a 16-minute YouTube video must be the least efficient way to store an equation. If only there was some sort of a 'fractal compression' method.
You can't shut us down! The Internet is about the free exchange and sale of other people's ideas!
It's not n^2 + n, it's n^2 + c.
That's to say, the number you multiply by itself isn't the same as the number you add.
Confucius say, "Find worm in apple - bad. Find half a worm - worse."
Mandelbrot Zooms Now Surpass the Scale of the Observable Universe
First off, does that even mean anything? What units is the "scale" of a universe expressed in?
Okay, let's take it to mean the ratio of the size of observable universe to the size of the Planck length, for lack of any better definition. In that case, Mandelzooms surpassed that years ago.
with no signs of loss of complexity at all.
You make it sound like we're expecting a loss of complexity, and we just haven't found it yet. But isn't it mathematically proven that the Mandelbrot set has the same "complexity" at all scales? Kind of inherent in the whole "fractal" thing, I thought...
I'd have thought it would be more interesting to talk about, for example, how all the pretty colours that everyone gawps at aren't even points in the set. They're just colour-coded as to how long the sequence takes to reach a certain value (all of the coloured points ultimately diverge to infinity, which is what makes them not part of the set).
systemd is Roko's Basilisk.
For most complex numbers the sequence will most certainly not converge to positive or negative infinity, whatever those mean. When dealing with complex numbers it only makes sense to talk about a single infinity, which is the point at infinity of the projective complex line (a.k.a. "Riemann sphere").
I read the book "Fun With Numbers" by Mir publications, Moscow in 10th grade. It talked about simple things like immensity of a number like pow(2,64) explained in a simple language a 10th grader could get. (pow(2,64) rice grains would need a barn 3 meter wide, 3 meters tall and several times the distance of Earth to Moon or something like that).
So Mandelbrot set could exceed the resolution of the known universe, by some version of the definition of these terms, in as little as 64 iterations.
sed -e 's/Chuck Norris/Rajnikant/g' joke > fact
persay
That's per se. Go and stand on the naughty step with "peak" guy from the previous post.
How can something which is just a pure number outscale something that's physical and has actual dimensions?
At the bottom of the
Holy crap, the internet is full of stupid. Your argument has no place in this discussion - there is no anthropomorphization of plants in describing the function of leaves. Just because evolution does not know where it is headed and does not have a "direction" or a "director" does not mean that body parts do not have functions.
Birds do in fact have wings in order to fly. They did not decide to evolve wings, nor did they have a manifest destiny to fly and therefore created wings, but the function of wings in most birds is to enable flight.
Plants use photosynthesis to create the sugars they need to survive. The leaves are where this happens. The function of the leaf is to present surface area to the sun for photosynthesis. This says nothing of evolution, intelligent design or anything else of the sort.
We are all now suffering from your sophomoric inability to understand simple concepts of language and distinguish between a discussion of thermodynamics and the absorption of external energy and a discussion of evolution. Damn, the internet is a cesspool of stupid of every kind.