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That fractal that's been up on my wall for years

551 点作者 chriskw3 天前

20 条评论

CliffStoll2 天前
Outstanding work and a delightful read.
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nico3 天前
Amazing insightful and thoughtful write up, thank you!<p>Loved the 3d visualizations<p>It reminds me of this thing I built some time ago while playing with recursive decimation to generate effects similar to fractals from any image<p>You can play with it here: <a href="https:&#x2F;&#x2F;jsfiddle.net&#x2F;nicobrenner&#x2F;a1t869qf&#x2F;" rel="nofollow">https:&#x2F;&#x2F;jsfiddle.net&#x2F;nicobrenner&#x2F;a1t869qf&#x2F;</a><p>Just press Blursort 2x2 a couple of times to generate a few frames and then click Animate<p>You can also copy&#x2F;paste images into it<p>There’s no backend, it all just runs on the browser<p>Don’t recommend it on mobile
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taeric3 天前
Holy cow, I was expecting a quick read. Wound up having to skim some, as I need to get some work today. Will be coming back to this to play with some. Really well done!
leni5363 天前
Got a bit nerd-sniped by this and came up with an L-system that fills out (I think) &quot;the wallflower&quot;:<p><a href="https:&#x2F;&#x2F;onlinetools.com&#x2F;math&#x2F;l-system-generator?draw=AB&amp;skip=&amp;axiom=A&amp;rule-1=A%3DA%2BB-A-AB%2B&amp;rule-2=B%3D-AB%2BB%2BA-B&amp;rule-3=&amp;rule-4=&amp;rule-5=&amp;width=400&amp;height=400&amp;iterations=4&amp;angle=90&amp;direction=left&amp;line-width=2&amp;padding=50&amp;background-color=rgb(0%2C%200%2C%200)&amp;line-segment-color=white" rel="nofollow">https:&#x2F;&#x2F;onlinetools.com&#x2F;math&#x2F;l-system-generator?draw=AB&amp;skip...</a><p>edit: On second thought, this probably generates the other fractal, but I&#x27;m not sure.
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Cogito2 天前
Thought I&#x27;d check the arithmetic for 2 two-digit numbers, and it works!<p>I expect 41+14 to be 12 (two right plus two up equals two right and two up).<p>Long addition in long form below uses:<p>&#x27;=&#x27; to show equivalent lines (reordering of terms (1+2=2+1), spliting numbers (41=40+1), adding single digits (1+4=22))<p>&#x27;-&gt;&#x27; for when the algorithm gives a digit<p>&#x27;&lt;&#x27; for when we move over a column<p><pre><code> 41+14 = (40+1)+(10+4) = 40 + 10 + (1+4) = 40 + 10 + 22 -&gt; 1s digit = 2 &lt; 4 + 1 + 2 = 22 + 2 = 20 + 2 + 2 = 20 + 41 -&gt; 10s digit = 1 &lt; 2 + 4 = 0 -&gt; done == 12 </code></pre> [edit] Just noticed the article has two different numbering systems, one where 10, 20, 30, 40 are clockwise and one where they are anticlockwise. In both, 1, 2, 3, 4 are clockwise. My addition is on the second, where 10s are anticlockwise (this is what is used in the addition table).<p>It still works in the alternative system (14+21 should equal 12)<p><pre><code> 14+21 =10+20+42 -&gt;2 &lt;1+2+4 =13+4 =10+3+4 =10+31 -&gt;1 &lt;1+3 =0 ==12</code></pre>
cies2 天前
I had this one up the wall (giant print) at a place I worked:<p><a href="https:&#x2F;&#x2F;raw.githubusercontent.com&#x2F;cies&#x2F;haskell-fractal&#x2F;refs&#x2F;heads&#x2F;master&#x2F;poster.pdf" rel="nofollow">https:&#x2F;&#x2F;raw.githubusercontent.com&#x2F;cies&#x2F;haskell-fractal&#x2F;refs&#x2F;...</a> [17MB, sorry Github]<p>It contains the Haskell code that produced it: <a href="https:&#x2F;&#x2F;github.com&#x2F;cies&#x2F;haskell-fractal">https:&#x2F;&#x2F;github.com&#x2F;cies&#x2F;haskell-fractal</a><p>Especially the `sharpen` function was interesting to come up with (I used some now-offline tool to do curve fitting for me): <a href="https:&#x2F;&#x2F;github.com&#x2F;cies&#x2F;haskell-fractal&#x2F;blob&#x2F;master&#x2F;fractal.hs#L38">https:&#x2F;&#x2F;github.com&#x2F;cies&#x2F;haskell-fractal&#x2F;blob&#x2F;master&#x2F;fractal....</a><p>Fun little project. :)
CBLT3 天前
Well written! Would you mind sharing how you came up with the &quot;middle out&quot; numbering system? I can never seem to come up with something this inspired when I&#x27;m doing math problems by myself.
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Tade02 天前
&gt; Deciding to delegate to a future version of me that knows more math<p>Relatable. Huge part of my decision on what degree to pursue was a list of problems (mostly linear algebra) I needed to solve, but didn&#x27;t have the guidance (and internet connection) to.
baq2 天前
This went much deeper and harder than expected. One has to admire the dedication.<p>Question to the author: what would you recommend to hang on my kid’s wall today?
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mckeed1 天前
Fun post! I drew the first 5 iterations by hand myself and I&#x27;m finding it easiest to think of as a self-similar coloring of a square tesselation.<p>If you start with the shape of iteration 3, it tessellates as a 5x5 square tile. Make an infinite grid of those tile shapes with one iteration 3 version in the center. Treat that center tile as the center square in the iteration 3 pattern and color the tiles around it according to how the 2nd and 3rd iterations were built of squares. This gives you the 4th and 5th iteration and you can continue to iterate on the coloring outwards to color the grid of tiles in the wallflower pattern.
tcshit2 天前
Nice writeup! I was hoping to see a photo of the fractal on your wall.. Nice link to Knuth video that I somehow have missed.
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cess112 天前
Nice writeup. The Heighway dragon of Jurassic Park fame is pretty neat too.<p><a href="https:&#x2F;&#x2F;en.m.wikipedia.org&#x2F;wiki&#x2F;Dragon_curve" rel="nofollow">https:&#x2F;&#x2F;en.m.wikipedia.org&#x2F;wiki&#x2F;Dragon_curve</a>
wistlo1 天前
This is so much better than reading the news.<p>Favorited—I&#x27;ll be coming back to absorb more, as my aging semi-fluency in engineering physics and SQL doesn&#x27;t help much with the notation I last saw in the 1980s.
Scene_Cast22 天前
I wonder if something similar can be applied to get a dither pattern with built-in level of detail adjustment.
867-53092 天前
well, that escalated beautifully
kragen2 天前
This is beautiful. Thank you.
entropicdrifter3 天前
Kinda looks like a propeller
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bdamm3 天前
That was fun.
mathfailure1 天前
Too much math.
matt32102 天前
Now make a tiling game engine that uses these!