Recursion Tattoo Ideas
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 Malconstant
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 Joined: Wed Aug 24, 2011 1:44 am UTC
Recursion Tattoo Ideas
(Hopefully this is an appropriate place for this thread, let me know if not, I'm a bit new to these forums. But I figure it's a safe bet that Mathematicians on an xkcd forum wouldn't mind a recursion thread. And also I figure if ever there was an internet forum that Douglas Hofstadter checks out, it's probably xkcd)
I'd like to get a tattoo involving recursion and I'm trying to think of clever ways of doing this. Preferably using the closed geometry of an arm (or fingers/torso/whatever if need be) to loop in on itself. So far I've come up with the following:
 A time vs. recursion graph on the arm that's tilted 45 degrees clockwise so that the actual line for the graph is just a straight band around the arm, thus making a graph which embeds itself inside itself indefinitely as the recursion axis increases.
 A time vs. r (standing for either recursion or space for a Minkowski diagram) that's not tilted on the arm with a 45 degree line (speed of light for Minkowski diagram). In order to make the line wrap in on itself, I'd make it a Fourier series expansion to some finite order so you can see some good sine wave components in there, and then it's defined to be periodic at a period of the arm circumference, naturally.
 For a textbased tattoo, I've got (sic): The following is a fine example of the liar's paradox, "
 And finally, it's harder to describe, but a backandforth sequence of i d/dx((1/i) d/dx(i d/dx((1/i) d/dx (i d/dx( back and forth making an arm band. This can come to represent two mutually recursive sets of numbers which define Cosine and  i Sine respectively, spelling out Euler's identity (this last one I used to define two mutuallyrecursive rings in group theory to propose with, the wife having Euler's identity as a tramp stamp).
So yeah, any ideas for other clever recursionbased tattoos?
I'd like to get a tattoo involving recursion and I'm trying to think of clever ways of doing this. Preferably using the closed geometry of an arm (or fingers/torso/whatever if need be) to loop in on itself. So far I've come up with the following:
 A time vs. recursion graph on the arm that's tilted 45 degrees clockwise so that the actual line for the graph is just a straight band around the arm, thus making a graph which embeds itself inside itself indefinitely as the recursion axis increases.
 A time vs. r (standing for either recursion or space for a Minkowski diagram) that's not tilted on the arm with a 45 degree line (speed of light for Minkowski diagram). In order to make the line wrap in on itself, I'd make it a Fourier series expansion to some finite order so you can see some good sine wave components in there, and then it's defined to be periodic at a period of the arm circumference, naturally.
 For a textbased tattoo, I've got (sic): The following is a fine example of the liar's paradox, "
 And finally, it's harder to describe, but a backandforth sequence of i d/dx((1/i) d/dx(i d/dx((1/i) d/dx (i d/dx( back and forth making an arm band. This can come to represent two mutually recursive sets of numbers which define Cosine and  i Sine respectively, spelling out Euler's identity (this last one I used to define two mutuallyrecursive rings in group theory to propose with, the wife having Euler's identity as a tramp stamp).
So yeah, any ideas for other clever recursionbased tattoos?
 doogly
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Re: Recursion Tattoo Ideas
There's also a thread over here to poke at, if'n ya like pokin:
viewtopic.php?f=2&t=9770
But yeah, your sine cosine thing seems good, apart from my having no idea how that is supposed to work.
viewtopic.php?f=2&t=9770
But yeah, your sine cosine thing seems good, apart from my having no idea how that is supposed to work.
LE4dGOLEM: What's a Doug?
Noc: A larval Doogly. They grow the tail and stinger upon reaching adulthood.
Keep waggling your butt brows Brothers.
Or; Is that your eye butthairs?
Noc: A larval Doogly. They grow the tail and stinger upon reaching adulthood.
Keep waggling your butt brows Brothers.
Or; Is that your eye butthairs?
Re: Recursion Tattoo Ideas
Wouldn't the obvious recursion tattoo be to have one that shows a picture of the place on your body that includes that tattoo?
 Malconstant
 Posts: 258
 Joined: Wed Aug 24, 2011 1:44 am UTC
Re: Recursion Tattoo Ideas
Damn, that tattoo thread is massive, but they didn't seem to get into recursion so I'll repost over there. If the good people want to take this down that'd be alright, I don't know how these things work here (does "merging" copy future thread posts, in which case this one can stand alone and also contribute to the greater thread?).
Yeah, that's definitely an option. Though it ends up being more "implied" recursion than actual (for infinite recursion at any rate, go hard or go home). The best of this idea that I've heard was a tattoo on my chest of me ripping off my shirt, embedded a couple times for good measure.
It's a pretty ridiculous way of describing sin and cos. But just take a Taylor series expansion of i sin[x] and cos[x] around x=0, and define two sets (C = the elements of the cos[x] expansion, and S = the elements of the i sin[x] expansion). From there it's possible to rewrite the definitions of C and S by mutuallyrecursively defining them, because their elements naturally build up in very similar ways. So you have something like
C = {1, x^2/2!, x^4/4!,x^6/6!,x^8/8!, ...}
S = {i x, i x^3/3!, i x^5/5!, i x^7/7!, i x^9/9!, ...}
Now for C, you can define C_n (the nth element of C) as C_n = (1/i) d(S_n)/dx , and you can likewise define S_n as S_n = i d(C_(n+1))/dx.
There are other ways you can describe the sets, but those work. And from there, you can just reiterate the process:
C_n = (1/i) d(S_n)/dx = (1/i) d(i d(C_(n+1))/dx)/dx = (1/i) d(i d((1/i)d(S_(n+1))/dx)/dx)/dx = (1/i) d(i d((1/i)d(i d(C_(n+2))/dx)/dx)/dx)/dx etc.
So for the arm band idea: i d/dx((1/i) d/dx(i d/dx((1/i) d/dx (i d/dx( I really meant the above line, but with this kind of representation which is something that's a lot easier to write down on paper. Here, lemme try out this fancy Math button thing.
[imath]i \frac{d}{dx}\left(\frac{1}{i} \frac{d}{dx}\left(  i \frac{d}{dx} \left( \frac{1}{i} \frac{d}{dx} \left(  i\frac{d}{dx}\left( \frac{1}{i} \frac{d}{dx} \left(  i\frac{d}{dx}\left( \frac{1}{i} \frac{d}{dx} \left(  i\frac{d}{dx}\left( \frac{}{} \right. \right. \right. \right. \right. \right. \right. \right. \right.[/imath]
That's better. And that'll look the same for S as for C, they only differ in which operation you begin with, so that's a nice symmetry. Here, while making this post all fancy, here's an image of what I meant with the Fourier series time vs. r graph, except probably with only one iteration on an actual tattoo:
And here are two other representations of Fourier series expansions of lines constructing a basic Minkowski diagram of two reference frames, which is just barely recursive enough (cyclic really, due to Fourier expansion) and compelling enough to be willing to include:
This is just a normal Minkowski diagram for two reference frames with additional lines drawn in to point out time dilation (nothing labeled)
This is a stylized version of the above Minkowski diagram.
Same graph as above, but the cyclic nature is drawn out, which has the consequence of making the graph totally unrecognizable as relating to a Minkowski diagram (that makes it artistic right?).
LaserGuy wrote:Wouldn't the obvious recursion tattoo be to have one that shows a picture of the place on your body that includes that tattoo?
Yeah, that's definitely an option. Though it ends up being more "implied" recursion than actual (for infinite recursion at any rate, go hard or go home). The best of this idea that I've heard was a tattoo on my chest of me ripping off my shirt, embedded a couple times for good measure.
doogly wrote:But yeah, your sine cosine thing seems good, apart from my having no idea how that is supposed to work.
It's a pretty ridiculous way of describing sin and cos. But just take a Taylor series expansion of i sin[x] and cos[x] around x=0, and define two sets (C = the elements of the cos[x] expansion, and S = the elements of the i sin[x] expansion). From there it's possible to rewrite the definitions of C and S by mutuallyrecursively defining them, because their elements naturally build up in very similar ways. So you have something like
C = {1, x^2/2!, x^4/4!,x^6/6!,x^8/8!, ...}
S = {i x, i x^3/3!, i x^5/5!, i x^7/7!, i x^9/9!, ...}
Now for C, you can define C_n (the nth element of C) as C_n = (1/i) d(S_n)/dx , and you can likewise define S_n as S_n = i d(C_(n+1))/dx.
There are other ways you can describe the sets, but those work. And from there, you can just reiterate the process:
C_n = (1/i) d(S_n)/dx = (1/i) d(i d(C_(n+1))/dx)/dx = (1/i) d(i d((1/i)d(S_(n+1))/dx)/dx)/dx = (1/i) d(i d((1/i)d(i d(C_(n+2))/dx)/dx)/dx)/dx etc.
So for the arm band idea: i d/dx((1/i) d/dx(i d/dx((1/i) d/dx (i d/dx( I really meant the above line, but with this kind of representation which is something that's a lot easier to write down on paper. Here, lemme try out this fancy Math button thing.
[imath]i \frac{d}{dx}\left(\frac{1}{i} \frac{d}{dx}\left(  i \frac{d}{dx} \left( \frac{1}{i} \frac{d}{dx} \left(  i\frac{d}{dx}\left( \frac{1}{i} \frac{d}{dx} \left(  i\frac{d}{dx}\left( \frac{1}{i} \frac{d}{dx} \left(  i\frac{d}{dx}\left( \frac{}{} \right. \right. \right. \right. \right. \right. \right. \right. \right.[/imath]
That's better. And that'll look the same for S as for C, they only differ in which operation you begin with, so that's a nice symmetry. Here, while making this post all fancy, here's an image of what I meant with the Fourier series time vs. r graph, except probably with only one iteration on an actual tattoo:
And here are two other representations of Fourier series expansions of lines constructing a basic Minkowski diagram of two reference frames, which is just barely recursive enough (cyclic really, due to Fourier expansion) and compelling enough to be willing to include:
This is just a normal Minkowski diagram for two reference frames with additional lines drawn in to point out time dilation (nothing labeled)
This is a stylized version of the above Minkowski diagram.
Same graph as above, but the cyclic nature is drawn out, which has the consequence of making the graph totally unrecognizable as relating to a Minkowski diagram (that makes it artistic right?).
 Attachments

 FT Minkowski1.pdf
 Same graph as above, but emphasizing the periodicity.
 (49.63 KiB) Downloaded 105 times

 FT Minkowski2.pdf
 Stylized version of the Minkowski diagram
 (25.32 KiB) Downloaded 101 times

 FT Minkowski3.pdf
 This is the normal Minkowski diagram situation of two reference frames that the other graphs play off of with Fourier series approximation.
 (3.61 KiB) Downloaded 97 times

 FT c.pdf
 Fourier series expansion of a 45 degree line (c in a Minkowski diagram)
 (17.28 KiB) Downloaded 124 times
Last edited by Malconstant on Wed Aug 24, 2011 4:00 pm UTC, edited 2 times in total.
Technical Ben wrote:PS, doogly, way to miss the point.
 doogly
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Re: Recursion Tattoo Ideas
Malconstant wrote:Yeah, that's definitely an option. Though it ends up being more "implied" recursion than actual (for infinite recursion at any rate, go hard or go home). The best of this idea that I've heard was a tattoo on my chest of me ripping off my shirt, embedded a couple times for good measure.
Yeah, that is a great idea.
LE4dGOLEM: What's a Doug?
Noc: A larval Doogly. They grow the tail and stinger upon reaching adulthood.
Keep waggling your butt brows Brothers.
Or; Is that your eye butthairs?
Noc: A larval Doogly. They grow the tail and stinger upon reaching adulthood.
Keep waggling your butt brows Brothers.
Or; Is that your eye butthairs?
Re: Recursion Tattoo Ideas
I'm not grabbed by these ideas, but it's not going on my arm so that's okay.
I suppose the logician in me would be mildly amused by " the preceding yields falsehood when infinitely repeated" wrapped around the arm if recursion is what you're after.
I suppose the logician in me would be mildly amused by " the preceding yields falsehood when infinitely repeated" wrapped around the arm if recursion is what you're after.
Re: Recursion Tattoo Ideas
You could write something like "get a life to get a girlfriend to" with "to" ending just before the beginning of "get". It would read "get a life to get a girlfriend to get a life to get a girlfriend to get a life to get a girlfriend to...".
Or the more classical dictionary entry: "Recursion: see Recursion."
Or the more classical dictionary entry: "Recursion: see Recursion."
"Ich bin ein Teil von jener Kraft, die stets das Böse will und stets das Gute schafft."
 Talith
 Proved the Goldbach Conjecture
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Re: Recursion Tattoo Ideas
There's always the infamous hand drawing a hand drawing a.....
replace the pencil with a tattoo needle and you're set.
replace the pencil with a tattoo needle and you're set.
 Malconstant
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Re: Recursion Tattoo Ideas
Giallo wrote: "get a life to get a girlfriend to get a life to get a girlfriend to get a life to get a girlfriend to...".
Ooo, That's a sad one. I feel that may be rule number 2 in avoiding longterm tattoo regret. Rule number 1 being irony.
Another idea for an arm/leg/finger band:
++++++++++++++++++++++++++++++++++++
tilt your head to the side and it becomes x^x^x^x^x^x^x^x^x^x^x^x^x^x^x^x^x^x^x... which is a kind of fun function to think about, along with its derivative. Probably not compelling enough for a tattoo, but oh well.
I tried to think of a way to work in a Klein bottle (because I guess mobius strips are too cliche for me, but one more dimension must be a ok), but I haven't been able to come up with an elegant way of doing it.
Talith wrote:There's always the infamous hand drawing a hand drawing a.....
That's not a bad idea. I was trying to think of ways of drawing in hands that are "drawing" my actual hands. Or maybe draw in a tiny Escher on my forearm, where we share my right hand (so a perspective shot I guess), and then with his left hand he could be "drawing in" our mutual right hand, though I feel that's also destined for regret. I'd definitely be down for a good (simple/elegant) Escherstyle optical illusion though, but that may diverge too strongly from mathematics to be worth getting into here.
Technical Ben wrote:PS, doogly, way to miss the point.
 doogly
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Re: Recursion Tattoo Ideas
Yeah, hand on hand with tattoo needles sounds pretty dope. I would not actually tattoo the wrist and hand though.
LE4dGOLEM: What's a Doug?
Noc: A larval Doogly. They grow the tail and stinger upon reaching adulthood.
Keep waggling your butt brows Brothers.
Or; Is that your eye butthairs?
Noc: A larval Doogly. They grow the tail and stinger upon reaching adulthood.
Keep waggling your butt brows Brothers.
Or; Is that your eye butthairs?
Re: Recursion Tattoo Ideas
Clearly my sad sentence was only an example. I used that sentence because I couldn't come up with anything better
"Ich bin ein Teil von jener Kraft, die stets das Böse will und stets das Gute schafft."
Re: Recursion Tattoo Ideas
Giallo wrote:You could write something like "get a life to get a girlfriend to" with "to" ending just before the beginning of "get". It would read "get a life to get a girlfriend to get a life to get a girlfriend to get a life to get a girlfriend to...".
Or the more classical dictionary entry: "Recursion: see Recursion."
better would be "work a job to earn some money to live a life to"
 Malconstant
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Re: Recursion Tattoo Ideas
AvatarIII wrote:better would be "work a job to earn some money to live a life to"
live a life to work a job? Your employers must love you.
How about a positive event chain one? something like "make someone else smile, brighten their day, now that person will want to"
Or use the Zach Weiner joke as an implicit premise: "Did you know that the word "recursion" contains the word "recursion" in itself?" with the actual tattoo being
Spoiler:
That'd be a fun one to turn into an arm/leg/finger band. I can appreciate the lack of subtlety.
Technical Ben wrote:PS, doogly, way to miss the point.
Re: Recursion Tattoo Ideas
Malconstant wrote:AvatarIII wrote:better would be "work a job to earn some money to live a life to"
live a life to work a job? Your employers must love you.
How about a positive event chain one? something like "make someone else smile, brighten their day, now that person will want to"
Or use the Zach Weiner joke as an implicit premise: "Did you know that the word "recursion" contains the word "recursion" in itself?" with the actual tattoo being
That'd be a fun one to turn into an arm/leg/finger band. I can appreciate the lack of subtlety.
yeah i had a feeling there was something off about it,
maybe better would be "get paid to work to live to get paid"
also if anyone is interested in where the recursion thing mal mentioned comes from
http://www.smbccomics.com/index.php?db=comics&id=2325
 Malconstant
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Re: Recursion Tattoo Ideas
AvatarIII wrote:maybe better would be "get paid to work to live to get paid"
Maybe, though I think the trap lies with "to work" I'm not sure it's possible to put that in an implicitly depressing message in a way that's like "yeah, that's why I'm doing it, my partial end game is the work itself."
Also I included the smbc link in the spoiler. The forum won't let me embed URL's (is that a threshold number of posts thing?) so I was trying to be discreet about posting to another webcomic while I'm still new to these forums. But of course you're quite right.
Technical Ben wrote:PS, doogly, way to miss the point.
Re: Recursion Tattoo Ideas
Malconstant wrote:AvatarIII wrote:maybe better would be "get paid to work to live to get paid"
Maybe, though I think the trap lies with "to work" I'm not sure it's possible to put that in an implicitly depressing message in a way that's like "yeah, that's why I'm doing it, my partial end game is the work itself."
Also I included the smbc link in the spoiler. The forum won't let me embed URL's (is that a threshold number of posts thing?) so I was trying to be discreet about posting to another webcomic while I'm still new to these forums. But of course you're quite right.
i guess, but i was going for "getting paid to work" as in "getting paid for the work" like "i got paid to mow the lawn"
and i quoted you before you edited in the reference, or the spoiler tag, and since i only read 2 web comics, xkcd and smbc, i knew what you were talking about, but i thought i'd link to smbc for you, and for the people that might not read it.
Re: Recursion Tattoo Ideas
Malconstant wrote: "make someone else smile, brighten their day, now that person will want to"
Nice
What about:
"...your eyes reflecting my eyes reflecting..."?
"Ich bin ein Teil von jener Kraft, die stets das Böse will und stets das Gute schafft."
Re: Recursion Tattoo Ideas
You could try jethro tull; "watching me watching you watching him".
Re: Recursion Tattoo Ideas
How about some kind of variation on Escher's "Drawing Hands", eg with the hands holding tattoo guns instead of pencils?
http://farm1.static.flickr.com/223/476543243_2eed08e3fc.jpg
http://farm1.static.flickr.com/223/476543243_2eed08e3fc.jpg
Re: Recursion Tattoo Ideas
you mean exactly what Talith said earlier in the thread?
i guess you were just posting a recursion of that post
Talith wrote:There's always the infamous hand drawing a hand drawing a.....
replace the pencil with a tattoo needle and you're set.
i guess you were just posting a recursion of that post

 Posts: 1
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Re: Recursion Tattoo Ideas
Get a tattoo that contains all the tattoos that contain themselves.
 Malconstant
 Posts: 258
 Joined: Wed Aug 24, 2011 1:44 am UTC
Re: Recursion Tattoo Ideas
GOD_Over_Djinn wrote:Get a tattoo that contains all the tattoos that contain themselves.
Hahahaha. I loved this. Although I read it as "get a tattoo that contains all the tattoos", and that's the one I actually want.
Technical Ben wrote:PS, doogly, way to miss the point.
Re: Recursion Tattoo Ideas
AvatarIII wrote:you mean exactly what Talith said earlier in the thread?
Oops. * blush *
How about http://mathworld.wolfram.com/TuppersSelfReferentialFormula.html, then?
 Malconstant
 Posts: 258
 Joined: Wed Aug 24, 2011 1:44 am UTC
Re: Recursion Tattoo Ideas
PM 2Ring wrote:How about http://mathworld.wolfram.com/TuppersSelfReferentialFormula.html, then?
Also delightful. I'll need to look over some GEB sometime, I recall there was a program written very much like that idea.
Technical Ben wrote:PS, doogly, way to miss the point.
Re: Recursion Tattoo Ideas
Malconstant wrote:PM 2Ring wrote:How about http://mathworld.wolfram.com/TuppersSelfReferentialFormula.html, then?
Also delightful. I'll need to look over some GEB sometime, I recall there was a program written very much like that idea.
On a similar note, you could have the source code of a program that outputs its own source code. Here's one in C which is also a palindrome:
Code: Select all
/**/char q='"',*a="*//**/char q='%c',*a=%c%s%c*/};)b(stup;]d[b=]d472[b)d(elihw;)q,a,q,q,2+a,b(ftnirps;)b(stup{)(niam;731=d tni;]572[b,",b[275];int d=137;main(){puts(b);sprintf(b,a+2,q,q,a,q);while(d)b[274d]=b[d];puts(b);}/*c%s%c%=a*,'c%'=q rahc/**//*"=a*,'"'=q rahc/**/
Re: Recursion Tattoo Ideas
If you are into that sort of thing you could go with a fixed point combinator.
Y f =
f ( f ( f ( f ( f ( f ( f ( f ( f ( f ( f ( f ( f ( f ( f ( f ( f ( f ( f ( f (...
Y f =
f ( f ( f ( f ( f ( f ( f ( f ( f ( f ( f ( f ( f ( f ( f ( f ( f ( f ( f ( f (...
EvanED wrote:be aware that when most people say "regular expression" they really mean "something that is almost, but not quite, entirely unlike a regular expression"
Re: Recursion Tattoo Ideas
Recursion; noun,f,(lat.):
Recursion
Recursion
As the great philosopher Socrates once said: "No."
Re: Recursion Tattoo Ideas
Ever since I read the GOD (GOD Over Djinn) narrative from GEB, I've thought that an illustration of the genies exactly halfway through the "moment" it takes for the genie to ask the infinite chain of metagenies (i.e., when there is an infinite number of genies summoned) with each genie a fraction the size of the last would make a pretty cool illustration. Wouldn't make a bad tattoo, either, I would suppose.
Blue, blue, blue
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