math art

2004-02-26 05:03:37 pm

Here is a sample of the fractal art i make when i'm in a good mood. This one took me about 1.5 hours to make. I hope you like it.

and i hope this works:

[EDIT]
well that didn't so try this:

i hate what .jpg does to fractals but i can'tuse the 1280*960 image with 100% quality.[/url]

Thread title:

Toozin

2004-02-26 05:06:04 pm

Not impossible

just highly unlikely

That's a weird looking fractal.

The Last Metroid

2004-02-26 09:48:23 pm

mmm... tripod...

Light of Day

2004-02-26 11:13:05 pm

It's not exactly what comes to mind when I see the wrod fractal, but I like it anyway.

skynes

2004-02-27 05:30:11 am

Tripods a pain. You can't remote access pics. That's why I gave the link to my site and not the pic... :P

fractic

2004-02-27 05:39:49 am

hmm i gues i have to make a page then. I mainly use that acount to share files with a friend. 20MB is more then hotmail's inbox limit.

The Last Metroid

2004-02-27 11:09:28 am

Hmm... trippy.

I like it.

fractic

2004-02-27 11:24:07 am

Quote from The Last Metroid:

Hmm... trippy.

I like it.

trippy? math is very down-to-earth ;)

The Last Metroid

2004-02-27 11:27:33 am

Quote from fractic:

Quote from The Last Metroid:

Hmm... trippy.

I like it.

trippy? math is very down-to-earth ;)

Only when you understand it.

skynes

2004-02-27 11:38:19 am

Remember - There are only 10 kinds of people... Those who know binary and those who don't!

nate

2004-02-27 12:09:00 pm

looks very biological.

Apple Juice

2004-02-27 12:11:52 pm

LOL! skynes! Funny stuff.

fractic

2004-02-28 04:27:37 am

Since i was very happy with my last fractal i decided to make a variation on it. I started out with the same fractal as last time but modified a lot of things. But the essence of the picture is still the same. You can find it on the same page. Plz tell me what you think

skynes

2004-02-28 02:13:19 pm

Enlighten me... What is a fractal? I know its mathematical shapes but mroe accurately what is it?

Light of Day

2004-02-28 02:28:13 pm

In laymans terms, it's a picture that if you zoom in on it you'll see the same picture repeated inside it. Of course, since it's exactly the same picture, you can zoom in on that and see the same picture inside that too. It basically goes on repeating itself inside itself forever. You can see it fairly easily in frantics avatar. The different triangles are different colours, so technically they're not the same, but imagine it was all one colour. Each of the coloured triangles is a smaller, possibly upside down version of the whole thing. You can also see that the same as the whole thing, each of these triangles can be split into other triangles which are smaller versions of the whole thing. And each of these can be split...

Where it links into maths is that fractals can be generated by mathematical formula, but as I've never officially covered fractals I can't go into an detail about that.

skynes

2004-02-28 02:32:46 pm

I see it now... It's pretty cool.

Only Maths I'm doing now is propositional logic, Zed, Prolog, Venn diagrams n stuff... Thigns that are involved in Software Engineering

fractic

2004-02-28 03:08:12 pm

Quote from Light of Day:

You can see it fairly easily in frantics avatar

huh who is frantic? Its fraCtic mind you ;) however your description of fractal is accurate enough. I'll try to explain how the fractals i use in my art are made. It requires a extreme amount of math do it precisly but i'll give a rough explanation.

first you need to know complex numbers. We mathematics thought of a new number called i which is the squareroot of -1 so i^2=-1. A complex number is in the form a+b*i in which a and b are "normal" numbers. they add up like this: (a+b*i)+(c+d*i)=(a+c)+(b+d)*i
and multiplication goes like this: (a+b*i)*(c+d*i)=ac+ad*i+bc*i+bd*i^2=(ac-bd)+(ad+bc)*i.

Now we get to work. We assign a complex number to the plane by setting out multiples of i on the vertical axis. Then we pick up a formula and run ever point in the plane through it. this way we get a row of complex numbers. If the row is convergent we paint the point black and its called inside the set. If the row is divergent we give it a color depending on how it diverged.

the most standard formula is:
x0=pixel (the point where we try to see wether its in or oustide the set)
xn=x(n-1)^2+x0 (next= previous^2 +first)
i've uploaded a tird picture on the page to show you what we get. Simple formula amazing result don't you say? Its called the mandelbrot set after the man who invented it. The colloring is done by determining how fast the row is diverging. In the top image i used that same colloring method in the background (the blue and white bits). The cyan parts and the black lines are however done in another way. There the coloring is done by determining how close the row got to a certain shape.

The program i used is ultra fractal 3 you can download a trial version of it at www.ultrafractal.com

[quote="Light of Day"]You can see it fairly easily in frantics avatar[/quote]

huh who is frantic? Its fraCtic mind you ;) however your description of fractal is accurate enough. I'll try to explain how the fractals i use in my art are made. It requires a extreme amount of math do it precisly but i'll give a rough explanation.

first you need to know complex numbers. We mathematics thought of a new number called i which is the squareroot of -1 so i^2=-1. A complex number is in the form a+b*i in which a and b are "normal" numbers. they add up like this: (a+b*i)+(c+d*i)=(a+c)+(b+d)*i 
and multiplication goes like this: (a+b*i)*(c+d*i)=ac+ad*i+bc*i+bd*i^2=(ac-bd)+(ad+bc)*i.

Now we get to work. We assign a complex number to the plane by setting out multiples of i on the vertical axis. Then we pick up a formula and run ever point in the plane through it. this way we get a row of complex numbers. If the row is convergent we paint the point black and its called inside the set. If the row is divergent we give it a color depending on how it diverged.

the most standard formula is:
x0=pixel (the point where we try to see wether its in or oustide the set)
xn=x(n-1)^2+x0 (next= previous^2 +first) 
i've uploaded a tird picture on the page to show you what we get. Simple formula amazing result don't you say? Its called the mandelbrot set after the man who invented it. The colloring is done by determining how fast the row is diverging. In the top image i used that same colloring method in the background (the blue and white bits). The cyan parts and the black lines are however done in another way. There the coloring is done by determining how close the row got to a certain shape.

The program i used is ultra fractal 3 you can download a trial version of it at www.ultrafractal.com

skynes

2004-02-28 04:23:09 pm

u just blew my mind....

Metroid Prime

2004-02-28 04:25:21 pm

Quote from skynes:

u just blew my mind....

At least I'm not the only one. Embarassed

Light of Day

2004-02-28 04:54:31 pm

Quote from fractic:

Quote from Light of Day:

You can see it fairly easily in frantics avatar

huh who is frantic? Its fraCtic mind you ;)

Oops, sorry about that. Embarassed

Quote from MMcLean54:

Quote from skynes:

u just blew my mind....

At least I'm not the only one. Embarassed

So I must be the only one to understand it fully and clearly, huh? I should have know complex numbers would sneak in somewhere, it seems like they get in everywhere if you look hard enough. But finally, after knowing of it for years, the mandelbrot set gives up its secret. And it's rather anticlimactic. It's funny, though, how such a relativly simple formula gives such a comlex-looking picture, while fractics decptively simple looking avatar probably has a much more complicated formula.

ShadowMagus

2004-02-28 06:07:11 pm

Fractic... what kind of math class do you learn this in, so I can avoid it at all costs. Also, what are you majoring in?

Bleh, I get to go to University in the fall...

fractic

2004-02-29 03:20:03 am

First year university maths. But if you do any exact study you get complex numbers.

Metroid Prime

2004-02-29 09:42:48 am

Quote from Light of Day:

Quote from MMcLean54:

Quote from skynes:

u just blew my mind....

At least I'm not the only one. Embarassed

So I must be the only one to understand it fully and clearly, huh? I should have know complex numbers would sneak in somewhere, it seems like they get in everywhere if you look hard enough. But finally, after knowing of it for years, the mandelbrot set gives up its secret. And it's rather anticlimactic. It's funny, though, how such a relativly simple formula gives such a comlex-looking picture, while fractics decptively simple looking avatar probably has a much more complicated formula.

I just didn't understand the math part. Wink

fractic

2004-02-29 03:49:34 pm

Actually the math behind my avatar is completly different. It works with affeine transformations (quite bloody complicated!). But basically it just tells where and how the fractal should look like itself. But the math behind it is probably a lot more complicated

[EDIT]
ow btw i've uploaded a new image to the page. Give my your opinions plz

skynes

2004-03-01 05:51:57 am

I'm just happy sticking with programming! The Maths I do here is enough. Zed, Prolog, Venn Diagrams, Propositional Logic.

I wanna do no more!!!!