## Nice graphs?

For the discussion of math. Duh.

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Azrael UK
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Joined: Wed Oct 01, 2008 5:34 pm UTC

### Nice graphs?

Does anybody know of any cool-looking graphs? I spent ages playing with the superellipse formula yesterday, and having [imath]n\propto{}\sin{k}[/imath] and increasing k. (The result is a rectangle whose sides bulge in and outwards). Can anybody point me towards some more complex ones?

Sungura
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### Re: Nice graphs?

Use polar coordinates with different trig functions can get you hearts to flowers and a whole bunch of other neat stuff - my brother used to draw pictures with graphs all the time. Parametric curves (I think that is what they are called) also can produce some very pretty results. Try things in 3D too

Here is a site with a whole bunch of things you can do.
http://demonstrations.wolfram.com/topic ... hod=recent
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Bullislander05
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### Re: Nice graphs?

Try the Cornu Spiral. It's the third graph on the right on: http://en.wikipedia.org/wiki/Cornu_spiral

I like it.

z4lis
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### Re: Nice graphs?

Just zipping through wikipedia, looking for one...

http://en.wikipedia.org/wiki/Weierstrass_function

I found this one: http://en.wikipedia.org/wiki/Theta_function and I think it's rather pretty.

My calc professor said something about... a non-measurable and additive function (that is, f(a+b)=f(a)+f(b)) is dense in the plane, so the function sort of covers up the whole plane with a cloud of points, which I find rather fascinating. But I don't know what "non-measurable" means...
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mordacil
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### Re: Nice graphs?

The polar graph of Riemann's zeta function (picture here) looks pretty neat.

eltriuqS
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### Re: Nice graphs?

i tried the following in polar coordinates, but didn't get the exact result i wanted..
3(1-abs(sin(abs(x+pi/2)/2)))
sin(0.5abs(abs(x-1.5pi)-pi) )*2
abs(abs(x-1.5pi)-pi)
abs(abs(x-1.5pi)-pi) ^0.6
abs(abs(x-1.5pi)-pi) ^1.4

ConMan
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### Re: Nice graphs?

pollywog wrote:
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evilbeanfiend
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### Re: Nice graphs?

in ur beanz makin u eveel

RedWolf
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### Re: Nice graphs?

Sungura wrote:Use polar coordinates with different trig functions can get you hearts to flowers and a whole bunch of other neat stuff - my brother used to draw pictures with graphs all the time.

I was actually messing around with this earlier this year, and came up with something that vaguely resembled a dragonfly by graphing tan(tan(tan(x))). The exact number of tangent functions I used, I can't remember, however.

Lancashire McGee
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### Re: Nice graphs?

mordacil wrote:The polar graph of Riemann's zeta function (picture here) looks pretty neat.

I was very pleased to be able to program my TI-83 to make this happen.

GBog
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### Re: Nice graphs?

But... how?

Bretteur
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### Re: Nice graphs?

RedWolf wrote:
Sungura wrote:Use polar coordinates with different trig functions can get you hearts to flowers and a whole bunch of other neat stuff - my brother used to draw pictures with graphs all the time.

I was actually messing around with this earlier this year, and came up with something that vaguely resembled a dragonfly by graphing tan(tan(tan(x))). The exact number of tangent functions I used, I can't remember, however.

I came up with something similar a while ago. I didn't use tangent though, I used this:

(sin^4(4x) + cos^4(5x)) * (sin^8(5x)+cos^2(2x)+sin(3x))

Or rather, I made those two as separate functions r1 and r2 and then made r3 r1*r2. That made it a bit easier to experiment.

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### Re: Nice graphs?

Why bother with boring old functions when you can use Differential Equations?
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NathanielJ
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### Re: Nice graphs?

That becomes profoundly uninteresting (to the point of making me wonder why it even has a name, a wiki page, and/or is called self-referential) once you read about how it works.
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Lancashire McGee
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### Re: Nice graphs?

GBog wrote:But... how?

Basically, the program I wrote calculates every value of the Riemann Zeta Function for Zeta(1/2 +it), t between 0 and 35, inclusive, going by some tiny increment. After calculating, Pt-on(Re(z), Im(z)).

Place in oven, wait two to three hours, and presto! Delicious Zetacakes.

afarnen
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### Re: Nice graphs?

I'm surprised nobody's mentioned the graphs of fractals, like the Mandlebrot set for instance: http://en.wikipedia.org/wiki/Mandelbrot_set#Image_gallery_of_a_zoom_sequence

Here's a nice video of a Mandlebrot set zoom: http://www.youtube.com/watch?v=WAJE35wX1nQ&feature=related

Besides fractals, polytopes of dimension 4 and higher are pretty rad as well (though sometimes more intellectually stimulating than just pretty). Neat visualizations of various 4-polytopes: http://en.wikipedia.org/wiki/Convex_regular_4-polytope#Visualizations

susanspy
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Joined: Thu Mar 26, 2009 1:07 pm UTC

### Re: Nice graphs?

Hello all,

Thanks a million afarnen for the great comment, i was looking for what you have posted, i digged many places but ultimately found it here, happy to do so, please do post some cool links of videos like the once you just did.

Cheers!!!

Macbi
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### Re: Nice graphs?

NathanielJ wrote:

That becomes profoundly uninteresting (to the point of making me wonder why it even has a name, a wiki page, and/or is called self-referential) once you read about how it works.

The wikipedia article didn't explain it very well, does it just fill the entier plane with pixels such that any given picture has to be in there somewhere? If so, it's a lot more lame than I thought.
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### Re: Nice graphs?

${1\over 2} < \left\lfloor \mathrm{mod}\left(\left\lfloor {y \over 17} \right\rfloor 2^{-17 \lfloor x \rfloor - \mathrm{mod}(\lfloor y\rfloor, 17)},2\right)\right\rfloor$

The floor( y/17 ) extracts data stored in n.

mod( y, 17 ) extracts a value from 0 to 16 from the y coordinate.

K * 2^(-17x-mod( y, 17 ) )
moves the 17x+mod(y, 17) bit of K to the right spot near the decimal point.

K is floor( y/ 17 ) -- the data stored in n.

The mod operation then throws out the 'higher order' -- data too far away from the decimal point in the other direction.

< 1/2 throws out the 'lower order information'.

So ya, at location (binary encoding for a black and white image with 17 height)*17 in the y coordinate, it will graph that image.

This is a toy problem you throw at someone who writes a graphing package. But it is a funny toy.
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Last edited by JHVH on Fri Oct 23, 4004 BCE 6:17 pm, edited 6 times in total.

Torn Apart By Dingos
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### Re: Nice graphs?

I created the following graphs by accident (or, if you will, a mad experiment?!). Quothing myself:

Torn Apart By Dingos wrote:(From this thread: viewtopic.php?f=3&t=3366&p=66875&hilit=bat+curve#p66875 )

My first try was x=cos(t), y=sin(t)+cos(t)sin(1/cos(t)):

It became BAT CURVE!

But maybe something like (x sin(1/x))^2+y^2=1/2?

Coincidentally, it looks a lot like the Batman logo.