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February 26, 2007
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:iconmarkdow:
"So natralists observe, a flea
Hath smaller fleas that on him prey,
And these have smaller fleas that bite 'em,
And so proceed ad infinitum." Jonathan Swift

"Great fleas have little fleas upon their backs to bite 'em,
And little fleas have lesser fleas, and so ad infinitum.
And the great fleas themselves, in turn, have greater fleas to go on,
While these again have greater still, and greater still, and so on." Augustus De Morgan


An infinite dissection of the plane by logarithmic spirals.

There is a nice bistable perception in the animation: when I first see it, I percieve a wholistic pattern rotating clockwise and shrinking. But after a short time, I see half the contours as fixed, and the other half rotating (with no shrinking). Try fixating on a single edge point to experience the second percept.

The pattern is the basis of Orthologia trispiralis, and the pattern and transform is the basis for the animation Orthologia twist.

Here's the geeky description. It's a checkerboard division (8x2) of the plane by logarithmic spirals with a pitch of +/- pi/4 radians. The checkerboard is colored (orthogonal to the contours) by the first 2^3 = 8 elements of the Thue-Morse sequence, [0 1 1 0 1 0 0 1]. The relative phase between the two sets of opposite chirality spirals rotates through pi/2 radians; in this example the phase of one set is fixed.

MATLAB

[Broken link: A volume rendering derived from the animation, with the time axis transposed to a third spatial dimension.]


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There are no restrictions on use of this image. Claiming to be the originator or owner, explicitly or implicitly, is bad karma. A link (if appropriate), a note to dow@uoregon.edu, and credit are appreciated but not required.
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:iconvidthekid:
Mood: Amazed ~vidthekid Sep 20, 2007  Hobbyist Digital Artist
If I'd thought of this, I'd have used a simple alternating sequence instead of that Thue-Morse thing. But now I see that the apparent uneven spacing of the spirals resulting from that sequence gives the piece an overall more dynamic appearance.
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:iconpinto-warrior:
~Pinto-Warrior Sep 13, 2007
... mezmerizing

you made that in mathlab?
Ive heard lots ive good things about it... I only have mathematica...

Fav.
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:iconmarkdow:
~markdow Sep 13, 2007
Yes, Matlab ("matrix lab"), which was derived from Fortran-like syntax. Designed for easy use with arrays (like images), instead of math operations (Mathmatica). But they are similar in many respects.

Enjoyed a lot of your algorithmically generated stuff.
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:iconpinto-warrior:
~Pinto-Warrior Sep 13, 2007
thanks....

Yeah, its sounds like their functionality largely overlaps. So the images are rendered pointwize, wheras in mathematica they are generated based on primatives. btw, your avy is awesome! Ive been just staring at it for a while now....

Thanks. It takes a fair amount of thought to generate each image, which of course is true of any medium.
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:iconkidjet:
*kidjet Mar 22, 2007
Wow! Nice. :)
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:icondjsmalley:
~djsmalley Mar 21, 2007   Digital Artist
Very cool ~ !
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:iconshuiyue:
~ShuiYue Mar 17, 2007  Student Filmographer
Nice.
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:iconxeno-minako:
!Xeno-Minako Mar 17, 2007
Whoa...very amazingly done. ^^
I love how there ARE a pair of lines that don't move at all, yet the other moves exactly perpendicular to it.
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:iconmilamber55555:
~milamber55555 Mar 9, 2007  Hobbyist Digital Artist
TRIPPY!!!!!!!!!!!!!! I LOVE IT!!!!!!!!!
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:icongemstars:
~gemstars Mar 2, 2007
Urgh....I've been staring at this for too long! Far too long! I can see both ways, I've been trying to see how fast I can make it change back to the other way. Looking at it one way for a long time then saying 'Change!' ... the mind can be pretty stubborn, really. But it works. Wonderfully done. I liked your comment too, although your geeky explaination made my head go to goo... Well done, have a great day. :)
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