Fractals Revived

[itisally]

Found this and thought it was fasinating.

http://vimeo.com/18636293
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I could agree with you, but then we would both be wrong.

[The Potter]

With this one I have 366. One for each day!
Too bad the page break hides Legion's joke.
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Artwork | Fractals | Don't ignore your dreams; don't work too much; say what you think; cultivate friendships; be happy.

[The Potter]

It is my political statement.
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Artwork | Fractals | Don't ignore your dreams; don't work too much; say what you think; cultivate friendships; be happy.

[The Potter]

Shameless plug: Square One over in visitor games starts tomorrow! It will be fun
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Artwork | Fractals | Don't ignore your dreams; don't work too much; say what you think; cultivate friendships; be happy.

[The Potter]

There is something irresistible about branches of five.
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Artwork | Fractals | Don't ignore your dreams; don't work too much; say what you think; cultivate friendships; be happy.

[The Potter]

...ans the golden parts represent... everlasting joy?
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Artwork | Fractals | Don't ignore your dreams; don't work too much; say what you think; cultivate friendships; be happy.

[Buzzsaw]

.
Cool pictures, Matt, they look great. Here's a video to ck out, Mandelbrot Deep Set Animation - 15 2^969.
.

[The Potter]

That is impressive resolution, but I wish he had picked a more interesting area. The far left tip is very symmetric and for the most part rather boring. Usually I go to an area, find a little Mandelbrot and then explore from there. By doing this there are more details and generally more chaotic patterns.
I can only get to about 1e-27 before Fractal Domains gives out.


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Artwork | Fractals | Don't ignore your dreams; don't work too much; say what you think; cultivate friendships; be happy.

[Buzzsaw]

.
Okay, this one's not as deep but more complex.
Mandelbrot animation 14 2^208
.

[The Potter]

Better, but going to the edge of a small Mandelbrot is still the way to go. Or maybe I just like the self-symmetry of the mini-Mandelbrots.


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Artwork | Fractals | Don't ignore your dreams; don't work too much; say what you think; cultivate friendships; be happy.

[Buzzsaw]

The stills are beautiful.

[The Potter]

Today I will do something a little different. I took an image (known to me as 0604) and changed the resolution. I believe the 16th image is the exact same as image a few days ago. My choice for this series was rather arbitrary. The focal point stayed on 0.3869889274+0.5685893599i the entire time.


The color scheme doesn't work very well at first. Well, really any color scheme really won't be too interesting


Clearly we are heading near the large top blob!


Well, just outside that blob I guess.


And to a smaller Mandelbrot!


It is getting bigger...


And bigger...


So somewhere into the armpit I guess


Right into the biggest little blob!


Black areas mean long render times. But places near them are interesting!


Right into the spike! I love this image also.


Too far down doesn't usually get much better. So I picked a half-way point.


And now the variation begins.


Ooooooh a pretty spiral


Going into the spiral doesn't change much. So a detour


The patterns are now very interesting.





But I can go even farther!


Well, it doesn't look like much is ahead. But something is still there.


Just a few cracks in the sidewalk


Maybe something is ahead...


The patterns near the edge might be worth exploring.


But my point is surrounded by pepto bismol.
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Artwork | Fractals | Don't ignore your dreams; don't work too much; say what you think; cultivate friendships; be happy.

[Jedo the Jedi]

I think that was a much more interesting exploration of a fractal than most of the zoom videos I have seen. You explored the variation of the fractal rather than continually showing its similarities. If I understand you correctly, you find the variation to be much more interesting, and I agree with this notion.

Thanks for that awesome process!
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Paragon Tally: 18 mafia, 3 SKs (1 twice), 1 cultist, numerous chat scum...and counting.

[itisally]

I loved seeing the progression. It was very enlightening.
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I could agree with you, but then we would both be wrong.

[The Potter]

I wanted to create an organic reference, but despite the colors it is strangely inorganic.
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Artwork | Fractals | Don't ignore your dreams; don't work too much; say what you think; cultivate friendships; be happy.

[The Potter]

I bet the area close to that guy gets crazy
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Artwork | Fractals | Don't ignore your dreams; don't work too much; say what you think; cultivate friendships; be happy.

[Jedo the Jedi]

I get excited every time I see "The Potter" as the most recent poster of Off Topic. I love looking at a new fractal (almost) every day.

This one is particularly interesting. I have not seen such vibrant color concentrated around the black (I'm sure there's a specific name). Is there a specific mathematical difference here that causes this effect, or just how you tweaked the coloring?
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Paragon Tally: 18 mafia, 3 SKs (1 twice), 1 cultist, numerous chat scum...and counting.

[The Potter]

Black corresponds with the "trapped" portions. Usually I run about 15000 iterations. The break down is typically something like
0-1000 doesn't matter, nothing in the image escaped this fast
1000-5000 the place where color choice matters
5000+ the area in this region is so small that picking something dark and letting it blend in is best.

So in the image above--
0-500 is grey blue
1000 is the dark burgundy
2000 is the brighter purple
3000 is the bright cyan
8000 is a medium blue (you can see a little of it)
then there was a mix of reds and purples
And the black of the trapped region

So the sharp transition...really isn't that sharp!



A very similar approach was taken with this image.
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Artwork | Fractals | Don't ignore your dreams; don't work too much; say what you think; cultivate friendships; be happy.

[Jedo the Jedi]

I really need to go download my own program. I just haven't had the time to explore the options.
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Paragon Tally: 18 mafia, 3 SKs (1 twice), 1 cultist, numerous chat scum...and counting.

[The Potter]

Fractal Domains for Mac OS X
Fractal eXtreme, Windows (I have never used this software)

While on the Fractal Domains website, I noticed they had a store for prints. I would be happy to render any image to -any- size if someone wished to pay for the printing. I have done 36 inch @300 dpi renders for fun before but have yet to pay for the printing. I also always do 1440x900 versions for my collection of desktop pictures.



Winter
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Artwork | Fractals | Don't ignore your dreams; don't work too much; say what you think; cultivate friendships; be happy.

[Jedo the Jedi]

Desktop backgrounds! Genius!

When I have time to play around, I'll let you know how that program is. I might look for a few other options too.
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Paragon Tally: 18 mafia, 3 SKs (1 twice), 1 cultist, numerous chat scum...and counting.

[The Potter]

Yeah, I was getting tired of my old collection of ~280 after 6 years. Which is half the reason I got back into fractal spelunking.



Firework!
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Artwork | Fractals | Don't ignore your dreams; don't work too much; say what you think; cultivate friendships; be happy.

[The Potter]

I am not sure what to say.
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Artwork | Fractals | Don't ignore your dreams; don't work too much; say what you think; cultivate friendships; be happy.

[The Potter]

Blame the Fool and his Money when I start missing updates
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Artwork | Fractals | Don't ignore your dreams; don't work too much; say what you think; cultivate friendships; be happy.

[The Potter]

I like white these days.
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Artwork | Fractals | Don't ignore your dreams; don't work too much; say what you think; cultivate friendships; be happy.

[The Potter]

click on this link to see the real version

Awhile ago I my reply to one of the zoom movies was that the area was boring. I thought I should give a more in depth answer showing why.

Different areas of the Mandelbrot set branch in somewhat predictable ways. Each one of the black trapped regions trails out into a complex branching pattern. There are patterns in how many "main" branches exist.

The largest region, essentially the entire left side, doesn't really branch.
The second largest region is the top (and bottom) which branches into 2's.
The third largest region (mid right) goes into 3's
and this continues.

Also, the left side of the "spike" that boarders the trapped region has smaller trapped regions that also branch. The number of main branches increase linearly by the number associated with the spike.

The right side of the spike expands rapidly and I haven't had the chance to count enough to determine a pattern.
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Artwork | Fractals | Don't ignore your dreams; don't work too much; say what you think; cultivate friendships; be happy.

[The Potter]

As there were no comments, I will return back to the regular programming.



Something a little brighter!
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Artwork | Fractals | Don't ignore your dreams; don't work too much; say what you think; cultivate friendships; be happy.

[Jedo the Jedi]

I just forgot to type something. It was interesting. Thank you.
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Paragon Tally: 18 mafia, 3 SKs (1 twice), 1 cultist, numerous chat scum...and counting.

[The Potter]

I like to pretend that I have learned something useful about fractals. But I am still not sure what I really know.



Festive enough.
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Artwork | Fractals | Don't ignore your dreams; don't work too much; say what you think; cultivate friendships; be happy.

[The Potter]

It came from the zoom series.
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Artwork | Fractals | Don't ignore your dreams; don't work too much; say what you think; cultivate friendships; be happy.

[The Potter]

Let it not snow!
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Artwork | Fractals | Don't ignore your dreams; don't work too much; say what you think; cultivate friendships; be happy.

[The Potter]

An extra image to celebrate being a member almost 4 months!


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Artwork | Fractals | Don't ignore your dreams; don't work too much; say what you think; cultivate friendships; be happy.

[Scurra]

That last one has always been one of my favourites because you just know what you'll find when you head in towards the black blob near the middle of the line...

p.s. yes, thanks for these. I once worked (briefly) with a guy who helped co-create the fractal image compression file format (FIF) which I still think is one of the most impressive things I've ever seen.
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_{still Quiz Olympiad champion. Must get a life.
New definitions: COFFEE - someone who is coughed upon}

[Jedo the Jedi]

[The Potter]

I should get the software to make one of the zoom movies. At the end of the movie, I would go to a black spot... until a small rectangle appears. As it slowly grows larger the words Your Mom become clear. lolz!
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Artwork | Fractals | Don't ignore your dreams; don't work too much; say what you think; cultivate friendships; be happy.

[The Potter]

I hope to find something like this wash up on the beach someday.
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Artwork | Fractals | Don't ignore your dreams; don't work too much; say what you think; cultivate friendships; be happy.

[extropalopakettle]

I've used ultrafractal. The "trial" version puts watermarks on the rendered output, but it does animations - not just zooms, but parameter changes too. One cool animation to try: Zoom in down in the "crack" between two of the orbs of the main set. Make a duplicate of that, then in one window zoom down close to the tip of one of those tendril thingies on one side of the crack, and in the other window zoom down close to the tip of one of those on the other side. Copy their exact locations, and do a julia set animation with the start value parameter (forget what it's called) changing from the one location to the other. I'll see if I can put one together. In older versions of ultrafractal, I rendered individual images with a batch processor based on parameters generated by a script I wrote. I downloaded a new version and rendered an avi (took around 8 hours), but nothing plays it (I think the file size is too big - I did uncompressed).

[The Potter]

Instead of doing it on the main Mandelbrot I would recommend finding a small Mandelbrot. Then copy your file to get the necessary points. If you do this there will be more variations in the surrounding areas.



Feeling Irish today?
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Artwork | Fractals | Don't ignore your dreams; don't work too much; say what you think; cultivate friendships; be happy.

[Courk]

418 and 420 caught my eye. 420 for a Wii console, perhaps?

418, I don't know. It'd go good with something silver or pewter. I wonder if there's a place to make your own beer steins...

[The Potter]

OK, I'll trade 420 for a Wii console. Now it sounds like I am dealing drugs in a fractal thread. Would you like a larger version?
You can get custom beer steins. I don't know about metal ones embossed with fractals though.



A mellow day.
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Artwork | Fractals | Don't ignore your dreams; don't work too much; say what you think; cultivate friendships; be happy.