Whether you like math or not, you must concede that the Mandelbrot set is pretty cool. Despite being calculated from a very simple formula, it's literally infinite and endless. Even after countless zooming videos are posted on youtube every day, the total amount of set explored will always be 0%.The set was never invented, it was discovered. It always existed, but we can only see it now thanks to computers, and despite being known and studied since the 80s, there are still some mysteries surrounding it. For example it is known that the set is connected, and it is conjectured that the set is locally connected, but this has never been proven.Famous science fiction writer Arthur C. Clarke was fascinated by it and even made a documentary about it and fractals in general, going as far as adding a reference to the set in it's novel "The Ghost from the Grand Banks". Feel free to post images and facts about this wonderful set of complex numbers.
where did the set exist before computers started looking at it? was it floating out in space somewhere?
>>10646197>where did the set exist before computers started looking at it?it existed ...... IN THE FUTURE!! Is this proof Mandelbrot set transcends time and space?Unknown to the worlds top scientists, but we have yet to disprove it
>>10646215pretty sure the future is made up of things that don't exist yet.
>>10646197The ontological question of "what is math?">was it floating out in space somewhere?no.
Apart from the classic Mandelbrot set there are all sorts of even less explored but just as pretty variations like Julia sets.
>>10646291B...but godel thought mathematical objects are exactly like that
>>10646178There's no evidence it exists. Algorithmically generated pictures are not Mandelbrot set.
>>10647546there's no evidence you exist either, except for a fucking post on a screen which could me made up. and you know what? i'd rather the mandelbrot set exist than you. go fuck yourself.
>>10646197It existed as information in the akashic archive.
>>10647546but anon you can run the same formula in your favorite programming language and zoom in to verify they produce the same pictures at the same regions
>>10647546>no evidence it existsImagine being this retarded.
>>10647546Brograms as broofs :-D
>>10647546Well a way to see it for yourself is to download a computer program that generates pictures of the Mandelbrot set, you'll see not only that it generates such pictures, but that the diversity in such pictures is almost infinite, one can zoom as much as one wants, one can change parameters of the dimensions that the image does not show, and slowly the image will morf, will become something else, always continuously so, and giving you always a sense of fracticality, so sure they might be generated pictures but they do so in such a way that represents something with the traits of a mandelbrot set, though I imagine that with enough analysis you might conclude that it represents very accurately the mandelbrot set. But sure there's no indication that the mandelbrot exists in the same way (or say a very similar way) as an algorithmatically generated picture exists (assuming that one can reasonably speak about existence in terms of a similarity distance)
>>10647777And? I can watch anime on a computer, it doesn't mean 2D girls exist.
>>10648946>>10647546Some numbers are proven to be in the set, regardless of the number of iterations.
>>10647550shut up dumb baby
>>10646178The surface area of the Mandelbrot set is unknown but it's fairly small.
>>10646178What the hell is the application of the set anyway? What can you do with it? Not trolling, just curious. I remember "inventing" Cantor's Dust ages ago, but all I learned was that dimensional gradation is continuous. We have calculus for that.
>>10651072Math doesn't need an application.
>>10652208>formal scientistOh. I see. Very lovely shapes they are. Never mind then.
>>10652208>>10653011To be more precise, as with most things in abstract math, there may be an application but we just don't know what it is yet.
>>10646178In the early 90s when fractals & chaotic recursion first became calculable to interesting levels of detail by hobbyists, I collected and read books on the subject, but was frustrated by the lack of software, but around 2013 became obsessed with it when hardware and software got good enough to render 3D fractals. Now it's at the point where long 4K 3D animations, rendered within a reasonably short time, are feasible on budget of about 2K USD, so I'm about to pull the trigger on some hardware dedicated mostly to the purpose. Yet I still enjoy firing up the light & simple XAOS program to zoom around and make aesthetic finds, while wondering what the post-WWII abstract expressionists would make of all this, if the different streams of time could meet other than in the imagination.
>>10646217pretty sure you are wrong
>>10646178Is this our universes picture of the multiverse?
>>10651072For one, it and its related formulas are used in statistical studies and simulations of phenomena that exhibit chaotic behavior, in everything from the design of wireless devices to morphogenesis in multicellular organisms.
>>10653804This, of course. Were nature without regularity, science would be impossible, but if it were without surprise it wouldn't be necessary.
i want some silk mandlebrot inspired paisley shirts with trippy colors for the 2020 Dr. Thompson collection
>>10654095then you have a uselessly broad notion of existence
>>10651072This can be used to "create" true rand operators. You are looking at the basis of a "soul". If you can tap into the mathematical workings of this and apply it to encryption or artificial intelligence it could yield unprecedented results.
>>10655313>true rand operatorsLiterally no such thing. Nothing is random. It's all coincidence.
>>10655324So, you think freedom is an illusion?
>>10655331Obviously. So what?
>>10655336I'll remember you.
>>10655347This is a mandelbulb thread nowhttps://www.youtube.com/watch?v=TTpbP5BVtiAhttps://www.youtube.com/watch?v=cPbKP2ep05k
>>10646197 in the realm of formswhy hasnt anyone said this yeti thought people who like mathematics were all platonists
>>10654118Suppose I'll grant that. I don't see why a large statistical chunk of Brownian motion/noise would not serve just as well. Then again, I may be wrong.>>10655313Again, that sounds all well and good. But if I were to peg the problems of those applications to something, it wouldn't be "we're limited to using pseudo-random operators". But that's just my view.
>>10656089where does the realm of forms exist? is it floating out in space somewhere?
This is also in the mandelbrot set. Someone figured out how to get hyperbolic tilings in it.Bigger: https://www.deviantart.com/dinkydauset/art/Hyperbolic-Tiling-666434305
Have to reduce to 4K here
there was a dude what made a game where you race on the surface of an mutating 3d fractal, anyone know it?
>>10648912>Well a way to see it for yourself is to download a computer program that generates pictures of the Mandelbrot setAny recommendations?
>>10651072>What the hell is the application of the set anyway?Can be used to make fairly nifty t-shirts.
>>10657412For 3D there is Mandelbulber and MB3D, and for 2D there is ChaosPro, XAOS, and a commercial one called Ultra Fractal or some such thing. Some have dedicated download sites and others are to be found on SourceForge, which has tons of other freeware goodies.
>>10657399Vine sauce streamed it recently. Forgot the name.
One of the better NOVA episodes https://www.youtube.com/watch?v=HvXbQb57lsE
>>10656746 i dont knowim not a platonistits talked about like its 'higher' in some senseprobably not 'floating out in space somewherelike a 4th dimension i guess
>>10658990I'm confused. Are some of those sets actually located in the sections that seem completely black?
>>10659045The M set is a map of connected julia sets.
fractal zooms honestly spook the fuck out of me. the longer it goes on and the the border region is still just as complex and weird, the more i get uncomfortable
>>10659059I'm sorry, but I don't know if that answers my question. I'm asking if I could start at the top of the Mandelbrot set, zoom in on one of the areas that looks completely black, like the section where the red dot is in my image, and find the Julia set that they're indicating is there. In other words, are some of these sets completely surrounded by the 0 value or whatever it is called?
>>10659108Yes and no. Yes, with a point inside the M set you can generate that Julia set. No, you don't find it "zooming in".Actually you don't find any connected Julia set in the boundary of the M set, the ones you find are always Cantor spaces (not connected).