Double Spiral

(help my city!)

Conformal mappings are great: it's a very powerful branch of mathematics, which basically says you can deform almost any 2D object and transform it into something else while keeping the shape of objects the same (on a small scale). Hence this picture: you see no holes, no obvious distortion, but this image cannot be real. This trick is inspired by a painting by M.C. Escher: some Dutch mathematicians have found what the transformation is and explained it in (almost) layman terms.

In this particular case the image is twice repeated. In the parameterization discussed here, this is a (1,2) spiral
This image was done in The Gimp and transformed with MathMap.

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Comments

Matt Cline says:

This is a masterpiece. I'm still reading the texts and trying to figure out how to do it mathematically and how you did it in GIMP. This is truly one of the most extraordinary photos I have ever seen.

I am having one problem with the Math plugin. I try downloading it and opening it and my zip program says it can't read the file header. Any suggestions? (I'm using Windows).
Posted 37 months ago. ( permalink )

Seb Przd says:

Thanks! The file www.complang.tuwien.ac.at/~schani/mathmap/mat hmap-1.0.1.t... is a .tar.gz (unix archive) file. Winzip (or the equivalent in Windows) should be able to open it. Sometimes it happens that you download it and IInternet Explorer or Firefox transforms it into a .tar, but you saved it as a .tar.gz which confuses Winzip. Just rename it as a .tar.
If you succeed in compiling MathMap in Windows, let me know, because so far nobody has managed to do so with the latest version of MathMap...
Posted 37 months ago. ( permalink )

strollerdos says:

Wow seb - youve done the impossible AGAIN. continuously amazed by youre technical brillance and creativity.

PLEEEEAAASE set up a web page explaining how to do this stuff.
Posted 37 months ago. ( permalink )

Holliwell says:

that popping sound was my head exploding.

quality work seb
Posted 37 months ago. ( permalink )

!!! k2208 says:

wow
Posted 37 months ago. ( permalink )

fazfoto says:

Awesome.
Posted 37 months ago. ( permalink )

AKA33 says:

this is awesome
Posted 37 months ago. ( permalink )

lloydb says:

This is a great composition.
Posted 37 months ago. ( permalink )

1_drey says:

:-D
Cool!
Posted 37 months ago. ( permalink )

scovophoto says:

Very cool.
Posted 37 months ago. ( permalink )

And... Action! says:

Amazing!
Posted 37 months ago. ( permalink )

jozexit says:

coolnestest!! :]
math and photography.. yey!
Posted 37 months ago. ( permalink )

Stuck in Customs says:

Okay this is impossibly cool - I am in awe!
Posted 36 months ago. ( permalink )

AKA33 says:

blows my mind everytime
Posted 36 months ago. ( permalink )

duszyczkapl says:

amazing!!! fav
Posted 36 months ago. ( permalink )

mediocre says:

That is brilliant!
Posted 35 months ago. ( permalink )

francois et fier de l'Être says:

C'est génial, purement génial.
Please add to

(gallery & instructions)
Posted 33 months ago. ( permalink )

M J M says:

Great work, such depth!
Posted 32 months ago. ( permalink )

Josh Sommers says:

Simply amazing. Great Droste Effect.
Posted 32 months ago. ( permalink )

breic says:

Seb, this looks like what gadl calls a (p1,p2)=(2,1) parameterization for his recursive chessboard. (His (1,-2) chessboard looks rather different.) But then your convention agrees with the authority.
Posted 32 months ago. ( permalink )

Donderwolkje says:

wow this is too cool, need to learn this
Posted 30 months ago. ( permalink )

lynetter says:

I love photos like this, they remind me of escher drawings. Thanks too for sharing it under creative commons. I used it in my quote mashup set. Hope this is OK, let me know if not. :-)
www.flickr.com/photos/lynetter/376632696/in/s et-720575941...
Posted 30 months ago. ( permalink )

Diego M says:

your work remember me ESCHER
Posted 29 months ago. ( permalink )

antonioVi says:

Outstanding photo, made with open source software. Please consider posting it in:
Open Source Photography (OSP)
Posted 29 months ago. ( permalink )

roddh says:

wow! wonderful image. beautiful!
very interesting construction.
Posted 26 months ago. ( permalink )

mortimer? says:

A year ago today! great!!

--
Seen on the explore page. (?)
Posted 25 months ago. ( permalink )

Seb Przd says:

Thanks for the heads up mortimer!
(and if you are not bored with it yet, help my city!)
Posted 25 months ago. ( permalink )

24 Hour Humanity says:

funny picture :)
Posted 25 months ago. ( permalink )

mvongrue says:

Worth bringing it to the front page again. I did not see it so far. Currently I am thinking what to do with the droste effect....but still awating the right sujet.

Great shot
Regards
Markus
Posted 24 months ago. ( permalink )

photomastergreg says:

Another great work! I'm glad I found your pix!
Greg
Posted 23 months ago. ( permalink )

megbclemens says:

Hi, I'm an admin for a group called CCSPreC08, and we'd love to have your photo added to the group. We are a PreCalculus class that is putting together a group of photos with a math theme
Posted 16 months ago. ( permalink )

`^Ashepsut`^ [ away ] says:

Bellissima foto. Sarei lieta di poterla ospitare nel neogruppo
"Girandole e spirali". Se ti va, inviala a: www.flickr.com/groups/in_giro/

Posted 16 months ago. ( permalink )

C4T4 says:

Complimenti da Girandole e Spirali!
Mi farebbe piacere condividere la tua foto nel mio gruppo.
GIRANDOLE E SPIRALI
Se vuoi , invia la tua bella immagine e commentane almeno una.

Compliments from: Windmills & Spirals!
Please post this beautiful image to the group and comment on 1.

Posted 16 months ago. ( permalink )

AllieW (busy) says:

Just amazing!
Posted 13 months ago. ( permalink )

isavdmisa2 says:

bravissimo !
Posted 8 months ago. ( permalink )

hk_traveller says:

Hi, I'm an admin for a group called All Favourite Photos, and we'd love to have this added to the group!
Posted 8 months ago. ( permalink )

Goreki_ says:

Love it
it's like "Whirlpools" from Escher, I'm a huge fan
great work
Posted 7 months ago. ( permalink )

fotodiagramas says:

Hi, I'm an admin for a group called Fotografía Matemática, and we'd love to have this added to the group!
Posted 6 months ago. ( permalink )

mahlisuh says:

so cool!
Posted 3 weeks ago. ( permalink )

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	Part of: Flattening the Sphere

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Taken with a Canon EOS 300D Digital.
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Taken on July 7, 2006

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Double Spiral

Comments

Matt Cline says:

Seb Przd says:

strollerdos says:

Holliwell says:

!!! k2208 says:

fazfoto says:

AKA33 says:

lloydb says:

1_drey says:

scovophoto says:

And... Action! says:

jozexit says:

Stuck in Customs says:

AKA33 says:

duszyczkapl says:

mediocre says:

francois et fier de l'Être says:

M J M says:

Josh Sommers says:

breic says:

Donderwolkje says:

lynetter says:

Diego M says:

antonioVi says:

roddh says:

mortimer? says:

Seb Przd says:

24 Hour Humanity says:

mvongrue says:

photomastergreg says:

megbclemens says:

`^Ashepsut`^ [ away ] says:

C4T4 says:

AllieW (busy) says:

isavdmisa2 says:

hk_traveller says:

Goreki_ says:

fotodiagramas says:

mahlisuh says:

Would you like to comment?

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