
How to Fold a Julia Fractal - drudru11
http://acko.net/blog/how-to-fold-a-julia-fractal/?second
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sp4rki
I'm impressed with the explanations and everything... but what really got my
panties in a bunch is the visualization technology. That is one of the prime
examples I've seen of actually leveraging current web tech to communicate
actual content instead of just doing fancy stuff just because. I was initially
annoyed by the 3D header movement effect, but the content, graphs, and
animations of the actual content made me completely forget that and allowed me
to be bewildered by what we can do this day and age on the web. Congrats to
the maker!

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unconed
Consider the fancy header to be the first answer to: what happens when you put
a 3D engine inside a webpage. This article is what happens 12 months later...

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sp4rki
Hah I can relate to that! I will clarify something though, the effect is
really cool and I actually like it. What annoyed me is that I had initially
opened it and moved it to another pane (dwm here) and then when I moved it the
main panel I was using a smaller window than usual and when I scrolled I
couldn't hit any links, animation looked weird, and then I couldn't scroll
past the header.

I browsed it again in a floating window in a different tab (or space if you
wanna call it that way) where I keep a maximized chromium and I was no longer
annoyed :) Good job on being on the cutting edge though, that is something I
completely can appreciate.

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unconed
Sigh, every time my site hits hacker news or reddit I have to mention this...
it's a Webkit bug. I reported it 5 releases ago, it sits unloved and unfixed.
I imagine i'll just redo the site before they address it.

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sp4rki
Ohh that makes sense, I also wondered if it was Chromium in Linux thing so I
opened it up in Chrome in my work iMac and I noticed the same thing, albeit
less pronounced. It's very pretty when it does work so that kinda balances it
out. In any case your content is worth it, thanks again for the awesome sauce.

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daeken
Wow. I "understood" complex numbers, in that I could use them in specific
contexts in the past and got that they represented rotation, but this really
drove it home in a way that I could've used a decade ago. Great article.

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crazygringo
I am blown away by this intuitive explanation of _why_ Julia sets look the way
they do.

I was obsessed with the Mandelbrot and Julia sets waaaay back in high school,
with writing programs to produce them in real time, back on my 386. But I
never had the slightest understanding of _why_ they looked the way they do. So
to discover that now, almost 20 years later, is just amazing.

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randlet
I could have easily written this comment! My favourite programming memory of
all time was finally succeeding in turning the pseudo-code at the back of a
book[1] that my mom had bought me into a Turbo Pascal program that would
generate a Mandlebrot set. It was exhilarating!

[1] <http://www.amazon.ca/gp/product/0671742175/tag=canaamp-20>

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yesbabyyes
Me too - among my first, and best, programming experiences was turning pseudo-
code into QBASIC and marvel at the fractals and strange attractors growing on
the screen.

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crazysaem
I did so as well. I was fascinated that such a simple formula could produce an
infinitely complex image. To build it, I used Lazarus/Freepascal and
Wikipedia. It’s actually still hosted on Google code.

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metafunctor
If anyone is wondering how the visualizations were made, he has another
article about that here: <http://acko.net/blog/making-mathbox/>

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paulgb
> If there's interest, a future post could cover topics like: the nature of
> e^ix, [...]

I'm sure I'm not the only one who would be very interested.

Great work!

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xerula
I really enjoyed this too. Would love to see quaternions presented with a
similar treatment.

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dizzystar
Wow, simply incredible work. Stuff like this offers a glimpse into the future
of what the web can be and how it can be used to pass knowledge on. I knew
some of the concepts presented here, but I never knew what it all meant. Nice
touch in adding the equations as well. Beautiful presentation.

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0x0
This is the best use of 3d/svg(?)/html5 I've seen. Incredibly effective and
really beautiful.

Certainly did make my macbook air fan spin up like in the old days of flash
though ;)

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mars
this is webgl (at least the mathematical visualizations)

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sp332
For some reason the Mandelbrot fractal (slides 30 and 31 in the second part)
didn't render in Firefox but they worked in Chrome. Everything else seemed to
work fine.

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eric-hu
Thanks for pointing that out! I just accepted the black panes in stride
because the caption said "...this is not so easy to visualize"

I also noticed that the text of the page was angled away on page load in
Chrome, but not in FF

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mturmon
Beautiful work. This is a great marriage of medium and subject matter.

I particularly liked some of the the interpretations of the wave equation,
which were new to me.

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archivator
The actual graphics flash and disappear on my Linux Chrome 23 machine. The
header 3D shift works fine though.

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DuskStar
For me, it fails in both Chrome Canary (26.0.1378.2) and Firefox says I do not
have a compatible graphics card. (Possibly just hates my Optimus setup) And,
of course, IE9 lacks webGl in the first place, so it doesn't even get to the
point of causing a process hang like Canary did. All Windows 7.

Once I did find a browser that worked with the site, though- that's the best
explanation of both fractals and complex numbers I've ever seen!

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iamjochem
I am overwhelmed and feeling somewhat inadequate, such is often the case when
reading material posted on HN (I can't be the only one!).

truly a beautiful 'story', fantastic execution. bravo!

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vincentperes
wow! I heard many times that great mathematician can picture theories in their
mind... and that for some theories only few people on earth are able to
picture them. I always wondered if that's true and for people using math on
daily basis (mathematician or others) it's very important to picture what you
are trying to achieve or only numbers matter? Thanks!

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JonnieCache
It's more the case that the numbers and the mental picture are the same thing.
When I manage that kind of insight (rarely) that's what it's like anyway.

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altrego99
The square root animation, slide 29-30, is incorrect. It should not tear at
-i, it should tear at the direction of 1 instead. Other than that everything
else looks fine. Amazing work.

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unconed
By that point, the grid has been rotated 90 degrees, with the real axis on
top. This is mentioned in the notes.

I did this because it fits the letterbox layout more in the later transitions.

Edit: I changed it so this is made obvious.

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Crake
I loved this so much. The visualizations were beautiful, and I'm appreciative
of the effort that must have gone into such clear illustrations. The only
thing I would suggest would be to make the slide progression arrows somewhat
more eye-catching--I almost missed their presence entirely when I was quickly
scrolling down the page trying to parse whether or not I was going to read the
whole thing. As a result, I almost missed out on the defining part of the
experience.

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tim_hutton
Related: visualizing how the Mandelbrot maps onto itself:
<http://code.google.com/p/mandelstir/>

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the1
every time i visit webgl page, Xorg goes craz: (EE) [mi] EQ overflowing.
Additional events will be discarded until existing ev ents are processed.

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stuaxo
It may be worth working out what gfx driver you're using + posting a bug in
the relevant place.

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iharris
I would absolutely love to see more visualizations like this in e-textbooks. I
think it would assist with the readers' understanding, particularly in
secondary school math or physics where students may have difficulty grasping
new concepts in geometry, algebra, and the like. As a math tutor, having
something to show my students really helps things. Well done!

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fallous
I can only imagine this kind of excellent visualization combined with this
book: [http://www.amazon.com/Mathematics-Birth-Numbers-Jan-
Gullberg...](http://www.amazon.com/Mathematics-Birth-Numbers-Jan-
Gullberg/dp/039304002X/)

I'm pretty sure the result would be the utter destruction of my productivity
for a few years.

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lexy0202
Once you get over the 3D header this article is amazing.. the visualisations
are incredible.

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monochromatic
Based on the comments, this sounds like a great article that I'll have to
check out later... for the moment, however, all it does is crash Safari on my
ipad.

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drudru11
Yes, I suspect the mobile devices will not have the ability to display this
content. However, if you enable WebGL on Safari via the Developer menu, the
page will render really well on a Mac.

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mattmoss
This page was educational and interesting until it locked up my computer with
the CPU pegged full. Force power off/on "fixed" the problem.

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studio816
A hit of DMT will show you the world of complex numbers/geometric
patterns/higher dimensions that you can't even imagine in this 3D world.

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jcdavison
Really nice post, design and approach!

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jheriko
good stuff. :)

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IheartApplesDix
Awful website. Completely unnecessary design over substance, I couldn't even
change the URL to get away, I had to close the tab.

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dasil003
I was reading interestedly until my laptop fan got so loud I couldn't
concentrate anymore and had to shut it down. The room is now a degree or two
warmer.

