[HN Gopher] Fractal Geometry
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Fractal Geometry
Author : andsoitis
Score : 164 points
Date : 2024-05-28 03:41 UTC (19 hours ago)
(HTM) web link (users.math.yale.edu)
(TXT) w3m dump (users.math.yale.edu)
| inside_story wrote:
| I've always been interested in how fractal geometry can be used
| to survey and analyze networks of all kinds.
| (https://en.wikipedia.org/wiki/Fractal_dimension_on_networks)
|
| Interestingly enough, I'm now working on building intentional
| network interventions for tech in NYC-and it's called
| fractaltech.xyz
| kreelman wrote:
| Very cool. Thanks for linking this.
| RachelF wrote:
| For a while in the 1990's IFS (fractal) image compression was a
| serious competitor to JPEG.
|
| Microsoft Encarta used it on the encyclopedia CD-ROM.
|
| I don't know what happened to it. It was pretty slow to compress.
| bryanrasmussen wrote:
| a slow to compress format that does a good job sounds great for
| physical media which gets distributed, but sounds like it would
| be bad where the things being compressed are most probably many
| millions of individual images uploaded by users as you want a
| fast enough compression that you can start to return the
| compressed image to the user within milliseconds.
|
| That just sounds to me like what happened to it, although I
| can't say for sure - did it perhaps also have other things
| about it that would make it a problem to be running lots of
| concurrent fractal compressing processes on a server?
| RachelF wrote:
| I don't know - the machine I played with it on was a 16MHz
| 386, and the IFS software was not optimized. But it was way
| slower than DCT-based JPEGs to compress.
|
| The odd thing about it though, was that it could upscale
| smoothly. A 320x200 source could be decompressed at 640x400,
| and it would sort of intelligently "fill in the gaps" on
| textures etc.
| Zitrax wrote:
| Some comparison between fractal compression and jpeg here:
| https://dl.acm.org/doi/fullHtml/10.5555/364682.364685
| crazygringo wrote:
| Slow to compress in the 1990s is probably not that slow to
| compress in 2024.
|
| And you can always do fast initial compression on images
| needed immediately, and run background compression to replace
| them with the smaller versions.
| bryanrasmussen wrote:
| hmm, yeah I never thought about that (the second part)
|
| but slow to compress is always relative to fast to
| compress, and fast is related to user expectations of speed
| which is calibrated to your competitor's speed, thus if
| something is slow to compress it will probably stay slow to
| compress even as its speed increases.
| zimpenfish wrote:
| > I don't know what happened to it.
|
| From what I've heard, licensing costs were significant.
| crazygringo wrote:
| Presumably the patents are all expired now?
| zimpenfish wrote:
| I think they were patented in the early 90s which would
| mean they've expired by now, yeah. CPUs and whatnot these
| days would make compression faster but trying to convince
| people to switch to fractal compression now is undoubtedly
| a losing proposition.
| jerf wrote:
| Sometimes things aren't "bad" _per se_ , they just aren't _as_
| good.
|
| Wavelets seem to be another perennial also-ran in the image
| compression space. They work. They have the odd useful property
| here and there. They just aren't _as_ good for most purposes.
|
| There can also be differences in terms of investment; if
| hypothetically there were 3 techniques with roughly equally-
| useful "final forms", but only one of them gets that
| investment, then it'll win because there's no reason to pour
| the additional effort into the other two.
| mg wrote:
| I'm still surprised that only one mathematical form has been
| found with the beauty and depth of the Mandelbrot set.
|
| One would think that like in the physical world, there should be
| many "species" with different types of appearances. Each a
| beautiful system on its own, but in comparable complexity.
|
| Maybe the complexity of the Mandelbrot set is to the mathematical
| universe what is the complexity of life in the physical universe.
| Something that is very rare. For some unknown reason.
| zmgsabst wrote:
| What do you mean by "mathematical form" here?
| mg wrote:
| A way to colorize the two-dimensional plane.
|
| Nothing compares to the complexity of the Mandelbrot formula
| when it comes to colorizing the two-dimensional plane.
|
| With complexity I mean the human impression of complexity.
| The reaction of "Oh, there is a lot of stuff going on in
| there" after looking at some parts of it.
| FredrikMeyer wrote:
| There are _many_ fractals and variations of them. The
| Mandelbrot is definitely famous, but it is hard to say if
| it is "the best". Look for example at this strange
| creature:
| https://en.wikipedia.org/wiki/Burning_Ship_fractal
| zmgsabst wrote:
| I've never felt more staring at the Mandelbrot than, say,
| pendulum settlement patterns or random noise.
|
| Often less, in that the Mandelbrot set has much more
| regularity than those examples.
|
| I suppose we have different aesthetics.
| eigenket wrote:
| I think this isn't true (at least subjectively, for me). There
| are plenty of similar objects you can construct.
|
| This wikipedia page has a bunch of examples of Julia sets
|
| https://en.wikipedia.org/wiki/Julia_set#Examples
|
| I'm also partial to Newton fractals, some of which look very
| cool
|
| https://en.m.wikipedia.org/wiki/Newton_fractal
| a3d wrote:
| "andsoitis" added 36 points to get on top of the charts, Some
| deeper links seem broken - I suspect this is old website
|
| Fractals are old folly, patterns of nature - wonder if there are
| active use cases to represent data in some form of fractal models
| zmgsabst wrote:
| Wavelets are arguably a fractal representation.
| __rito__ wrote:
| If you are interested in learning about Fractals in form of a
| MOOC, I can highly recommend "Fractals and Scaling" from Santa Fe
| Institute [0]. It is very accessible and taught by David Feldman.
|
| [0]: https://www.complexityexplorer.org/courses/169-fractals-
| and-...
| kdfjgbdfkjgb wrote:
| MOOC: Massive Open Online Course
| lopis wrote:
| A bit of a tangential meta comment, but it's refreshing to see a
| cool website in 2024 like this, all content no fluff. I'm
| surprised to see it still using frameset. But also sort of sad
| that there's currently no HTML5 equivalent to have resizeable
| panels like this without messing with javascript, mouse events,
| and so many edgecases. Frameset still works in all browsers, so I
| suppose you could can just use that, although it's been
| deprecated for almost 20 years now.
|
| I understand that the purpose of HTML is not to support such
| functionalities, but CSS could have filled the gap. The closest
| we ended up getting was "resize" but it only affects one element.
| slowhadoken wrote:
| I've been reading about spatial partitioning of fractals lately
| but haven't found a good resource on the subject. They probably
| use bsp-trees?
| tevelee wrote:
| The link of paragraph '10. Panorama of Fractals and Their Uses'
| points to nonexistent content.
| bazzargh wrote:
| A lot of the broken links and images on that site work if you
| view it on the internet archive, eg the "Manufactured Fractals"
| images are mostly missing now, and the "Ineffective Ways to
| Measure" page is gone now, but still there in the archive
|
| https://web.archive.org/web/20151110050637/http://users.math...
|
| that "Panorama" page tho, remains broken. The source of the
| page on the archive says "ruffle-polyfilled" suggesting there
| was a flash animation there. I think a lot of it was probably
| the content behind the links of the "Manufactured Fractals"
| section - if you look you'll see those urls are all in the
| Panorama folder.
| nico wrote:
| Yesterday someone posted this awesome 3D fractal visualizer for
| the browser (it runs really well on my phone):
|
| https://news.ycombinator.com/item?id=40493981
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