Nice graphs?
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Nice graphs?
Does anybody know of any coollooking 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
Here is a site with a whole bunch of things you can do.
http://demonstrations.wolfram.com/topic ... hod=recent
"Would you rather fight a Sungurasized spider or 1000 spidersized Sunguras?" Zarq
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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.
I like it.
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 nonmeasurable 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 "nonmeasurable" means...
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 nonmeasurable 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 "nonmeasurable" means...
What they (mathematicians) define as interesting depends on their particular field of study; mathematical anaylsts find pain and extreme confusion interesting, whereas geometers are interested in beauty.
Re: Nice graphs?
The polar graph of Riemann's zeta function (picture here) looks pretty neat.
Re: Nice graphs?
i tried the following in polar coordinates, but didn't get the exact result i wanted..
 3(1abs(sin(abs(x+pi/2)/2)))
sin(0.5abs(abs(x1.5pi)pi) )*2
abs(abs(x1.5pi)pi)
abs(abs(x1.5pi)pi) ^0.6
abs(abs(x1.5pi)pi) ^1.4
Re: Nice graphs?
pollywog wrote:I want to learn this smile, perfect it, and then go around smiling at lesbians and freaking them out.Wikihow wrote:* Smile a lot! Give a gay girl a knowing "Hey, I'm a lesbian too!" smile.
 evilbeanfiend
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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 TI83 to make this happen.
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.
 headprogrammingczar
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Re: Nice graphs?
<quintopia> You're not crazy. you're the goddamn headprogrammingspock!
<Weeks> You're the goddamn headprogrammingspock!
<Cheese> I love you
<Weeks> You're the goddamn headprogrammingspock!
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 NathanielJ
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Re: Nice graphs?
ConMan wrote:Tupper's selfreferential formula
That becomes profoundly uninteresting (to the point of making me wonder why it even has a name, a wiki page, and/or is called selfreferential) once you read about how it works.
 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, Pton(Re(z), Im(z)).
Place in oven, wait two to three hours, and presto! Delicious Zetacakes.
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 4polytopes: http://en.wikipedia.org/wiki/Convex_regular_4polytope#Visualizations
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 4polytopes: http://en.wikipedia.org/wiki/Convex_regular_4polytope#Visualizations
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!!!
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!!!
Re: Nice graphs?
NathanielJ wrote:ConMan wrote:Tupper's selfreferential formula
That becomes profoundly uninteresting (to the point of making me wonder why it even has a name, a wiki page, and/or is called selfreferential) 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.
 Indigo is a lie.
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 Yakk
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Re: Nice graphs?
[math]{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[/math]
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^(17xmod( 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.
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^(17xmod( 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.
One of the painful things about our time is that those who feel certainty are stupid, and those with any imagination and understanding are filled with doubt and indecision  BR
Last edited by JHVH on Fri Oct 23, 4004 BCE 6:17 pm, edited 6 times in total.
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.
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