Fractals Revived

[Jedo the Jedi]

Grap? Is that what happens when you're in a closet with someone? Grapping?

Fractals are so beautiful. I knew math was good for something.

[MatthewV]

*jumps with new dage excitement*
p anb b anp d are all the same letter
Oh, I realizep that the contrast on the last few has been way too high. I have my monitor set at adout 50%...
The puzzle is now completed :)
Newton...

[MatthewV]

And the leaves that were green turn to blue-ishThe puzzle is now completed :)
Newton...

[MatthewV]

I don't really know...but it is...uhmmm
The puzzle is now completed :)
Newton...

[Jedo the Jedi]

Isn't there something like the Julia fractal? Do you know what I'm talking about? If so, can we get a pic of that? I don't mean to mess up any theme you've got going, but I'd like to see that.

[Bicho the Inhaler]

There's no "the" Julia fractal. If you take a function f on the complex plane, then for a given complex number z, consider the sequence f(z), f(f(z)), f(f(f(z))), .... For some values of z, that sequence will be "well-behaved" (for example, it will approach some limit a, or it will approach a periodic sequence like a, b, a, b, ... or a, b, c, a, b, c, a, b, c, ...). The "Julia set" (named after mathematician Gaston Julia) of the function f is properly the set of z for which this does not happen. Often, the Julia set is the boundary of some other set, and then the term gets slightly abused, and the set it bounds gets called the "Julia set" too.

I think most of the fractals so far in this thread have been "based on" the Julia set of some function. (Mandelbrot-like fractals would be one exception.)

[old grey mare]

Hmm.. I wonder.. If you look at a fractal while having an LSD acid trip, maybe it all cancels out and looks like an ocean sunset.
Dude, that would be trippy.

[MatthewV]

I did a few months of fractals from the Julia set. I would guess somewhere on page three of this thread.
The puzzle is now completed :)
Newton...

[MatthewV]

entering the eye...
The puzzle is now completed :)
Newton...

[Mackay]

#311: "Please, for the love of Pete, DO NOT feed Da Huuuuudge"

[MatthewV]

I've been having trouble with the whole counting thing...
The puzzle is now completed :)
Newton...

[MatthewV]

That purple thing was once under my bed!
The puzzle is unsolved :(
Newton...

[L'lanmal]

Edit:
Jedo, post 12 in this thread might help you out.

[MatthewV]

[MatthewV]

Bah, I responded to an editted post.

Approaching a strange horizon line!
Newton still...

[MatthewV]

Because Mackay is spamming off topic, I will update my fractal :)
Newton still...

[Mackay]

I am drunk and have fallen on the road. I can't see straight, but there are definitely some sets of headlights coming my way...

[One Skunk Todd]

Wow! I really like the newtons.

[MatthewV]

I like the figs :)
Newton still...

[Mackay]

I still see headlights coming from random directions... though this time I'm tripping on LSD and standing in the middle of the freeway.

[MatthewV]

[MatthewV]

Sort of a yang-ying feel
Mandelbrot rediscovered!

[Mackay]

It's like... a spreading stain of evil. Does that even make sense?

[MatthewV]

Leaves falling off alien trees
Mandelbrot rediscovered!

[Courk]

Here's the chair I decorated with one of the fractals:


It's a crappy picture, the chair is a lot brighter than that.

[zorT Kitty]

Courk, how did you do that? Thats awesome!


*wants one*

[Courk]

A simple four-step process: Print, cut, paste, shellac. Although, I added an extra step before print -- bug MattV for a larger image so the seat isn't a repetitive design.

The only part of the chair I prepped were the parts that got painted -- the rungs and the legs, since it would have been difficult to glue paper to them. All I did was sand and prime those, everything else still had varnish.

It's not a difficult thing to do. I used Elmer's glue to hold the paper in place. The paint was just acrylic and tempera. Once everything was painted and glued, I shellaced it quite a few times.

[MatthewV]

And step seven is repairing :-)
step six was bugging MatthewV again :-P

[Courk]

OK, it's a simple 7 step process: bug for fractal, print, cut, paste, shellac, remember where you put the fractal, touch up.

[extro...*..*.*]

[Courk]

How did you print it? Big paper, special printer? Or multiple sheets spliced together?

I just used the same paper I use to print everything. Looking at the package, I guess it's called copy paper. Then I just cut carefully along the borders, making sure all the white was removed, and lined them up carefully on the seat.

And what about the curves? How do you bend flat sheets around (what's the adjective for curves that flat sheets can't be bent around?) whatchamacallit curves?

I'm going to give a long answer and hope it answers your question at some point.

For the seat part the rungs come down and are actually on the seat instead of attached to the back, so I had to figure out where to cut holes for those. I made a template out of plain paper and traced it onto the fractal, then cut a slit up to the hole and cut out the hole. The slit will line itself back up perfectly, so you can only see it if you're looking for it.

I used 4 pieces of paper for the seat, but I think only one was a full sheet. If you locate the seams, the seat generally looks like this:

I placed the pieces on the seat dry, and traced gently underneath with a pencil around the curve of the chair. I then cut that out. There's a couple slight dips in the chair where your legs are located, but the paper handled those fine -- plus one seam was in the middle of the dip. The papers for the top of the seat part were just used for that part -- I didn't fold them over for the edge of the seat. For the edge I basically used a strip of the fractal to go around. For the most part it was all one width. At the front there was a bit of a dip then rise, but that was involved with the width of the paper, not the bending (if that makes sense). I don't know how many individual strips I had to use to go around.

As I said earlier, the rungs were painted (I was not going to try to make a piece of paper bend around those). I recommend acrylic paint -- it seemed like the tempera paint I used cracked, but that might be because I didn't use enough shellac and buttons and the like rubbed against it for a year.

For the top of the back of the chair, I worked much like I did on the seat -- I made sure the pieces fit, then I traced around the curve of the chair to see what I didn't need. Except this time I cut larger than what I traced by about an inch along the top and side -- the bottom I cut even. The amount you leave extra depends on the width of the chair. On this extra inch, I cut slits down to the trace line so that there were little flaps, about an inch each in width, all along the paper. When I glued the paper down, I folded all the tabs over to the sides and behind the back and glued them down. Behind the back of mine I already had a piece of paper glued down that was cut even all around, so the tabs were on top. It's busy enough on the back that you can't tell, but you could easily glue the tabs down then add the evenly cut piece to hide them. Along the top edge of the back of the chair there were tiny little slivers of wood showing through because of the way the chair curved and the flaps. I just added bits of scrap fractal images underneath these cracks and put the flaps over them.

Here's a picture of what the paper for the front part of the back of the chair looked like:
Black is the trace line and red lines are cutting lines.

A note on gluing: I used school glue spread thin with an old paint brush (to avoid glue bubbles). It likes to dry fast when it's spread that thin, so carefully place the paper down. If you make a mistake you can very carefully peel it back up, but it'd probably be best if you put down another layer of glue before you reset the piece. I was touching up the seat this weekend by adding another piece of paper over the site that wore out, and I didn't line it up quite right, so I peeled it off and expected it to stick with the original glue because I thought it would save time. It was held in place, but not very securely, and when I added shellac it lifted up off of the seat. I had to peel that piece off and start over.

Also, make sure the middle is sticking. You can always get corners that are sticking up with a bit of glue on a paint brush, plus teeny tiny corners that stick up will probably be held down by the shellac.

I hope all of this made sense. Let me know if you have any other questions or if I didn't make sense.

[The Potter]

I am working at uploading all the images to glpics again. I have been using my fractal collection as desktop pictures for about 6 years now!



Time to finish the 366 image set. I have about 80 to go I believe.

[The Potter]

Funny... I made an image with the number of 0421 but the original image source file was lost. So the last image and the new one appear the same but are different! Or something.

[The Potter]

The newer version has an easier to use color editor.

[Jedo the Jedi]

I forgot how beautiful these are to look at. Thanks for bumping the thread!

How do you supply the color?
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[Mackay]

Hell yeah fractal thread!

LOVE the latest

[The Potter]

The colors fall in two categories first, In and Out. All the points that, after a 1000 or so iterations didn't reach a radius of 2, are bound and part of the M-set. They are colored black.

All the points that do reach the specified radius do in it Y sets-- somewhere between 0 and 1000. So every point can have a number attached to it. I made it in 876! I made it in just 432! It too me 765. And then colors are applied based on the numbers.

So after reading your post, I started to play with the escape radius. Normally I used the default of 2-- it has the same results of any number 2 or higher. And it is a good default number. But I started playing with escape radii in the 0.9 to 1.1 range.


This one was made before I messed with the escape range.


This one came afterward. Also note that I started making things a bit bigger. 1.5 times bigger!

[extropalopakettle]

A lot has happened in the computer-generated fractal world since the Mandelbrot set. Particularly interesting is the 3-Dimensional variant, the "mandlbulb", and programs for plotting it and other 3D fractals. Do youtube searches on 'mandelbulb' and 'mandelbox'. A lot of amazing variety. For instance:

http://www.youtube.com/watch?v=jYsbFreUMkg

http://www.youtube.com/watch?v=VTiI2g58zfU

http://www.youtube.com/watch?v=Yb5MRbgNKSk

http://www.youtube.com/watch?v=bKknJvZIn24

[The Pottery*]

And here I am being stuck in my ways. Engineers are cursed like that.

[Jedo the Jedi]

I read back through the thread to re-learn what a fractal is, and I realize I still don't know shit about them. The math is really just beyond me. (With a bit more basic learning, I'm sure I could come to understand, but I don't have any basis for terminology and such. Pre-Calc 8 years ago was my last stop for mathematics.)

Anyway, it does fascinate me how pure math can create such stunning art.
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