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Another recursive process I've come up with recently-- this one works on any polygon larger than 8. This instance uses nonagonal symmetry.
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20 triangles, 20 circles.
Wei Fu mentioned this model in one of their photos, and I have been thinking about it all day! I found a recursive folding method after a couple hours of doodling, and will probably retry with nicer paper sometime in the future.
The original is here: www.flickr.com/photos/samplesizeofone/7387973196/
Re: Peet's.
This is an example of the "Droste effect" (a.k.a., mise en abyme): a picture repeatedly appearing within itself (visual recursion).
The head of Romanesco broccoli is a visually striking example of an approximate fractal in nature. The pattern is only an approximate fractal since the pattern eventually terminates when the feature size becomes sufficiently small. In computer graphics, its pattern has been modeled as a recursive helical arrangement of cones.
The number of spirals on the head of Romanesco broccoli is a Fibonacci number (Wikipedia)
en.wikipedia.org/wiki/Romanesco_broccoli
www.wired.com/wiredscience/2010/09/fractal-patterns-in-na...
I admit it - I am a Photoshop addict. I get as much fun in the cutting room, as I do at the shoot.
So my favourite place also qualifies for today.
I installed an Adobe Labs free plugin called Pixelbender.
Then you can add your choice of filter into Pixelblender. Most of them are for special effects, so one has to wonder about how much use they really are.
This is the Droste filter and Adobe describes it as
A powerful filter to recreate Escher's Droste Effect where the image recursively repeats itself as a spiral. It will work with the Photoshop CS4 plugin or directly in After Effects where some mind boggling animations are possible!
The filter is not actually supposed to create a result like this, but rather a spiralling effect, but there are many buttons to push and while I did get a spiralling effect, it wasn't good so I kept playing. It may depend on the subject matter in the original.
Favourite Places Theme
Inspired and made possible by all the members of the Escher Print Gallery group. Done with the GIMP and Mathmap.
Escher's Droste Effect
EXPLORE on November 19, 2008 #295
http://slayer925.deviantart.com/art/Where-is-my-coffee-104237074
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See more photos and abstract drawings in my gallery on DeviantArt:
Thank you!
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Made with Mandelbulb 3d
See more photos and abstract drawings in my gallery on DeviantArt:
Thank you!
Where the deep dream generator found each shape that looked like itself and imposed it, scaled-down within the shape it resembled.
Structure Synth / Sunflow
The Structure Synth EiesenScript was generated by a ruby script, then tweaked a bit before exporting to Sunflow.
The model of the entrance to the model village. Inside, there's a full model of the model village, which, naturally, recursively contains a model of the model of the model village and so on.
Myself when young did eagerly frequent
Doctor and Saint, and heard great Argument
About it and about: but evermore
Came out by the same Door as in I went.
The Rubaiyat of Omar Khayyam
Recursive self portrait(s) -- in an 'electronic infinity mirror' or Time Warp. It is definitely the result of a single digital take (no cutting & pasting). The very observant may notice an untidy clue as to how it was done...
(A dozen nominated faves to anyone who picks this up. To be fair, you would need to be familiar with iPhones and the Apple ecosystem..)
It is a single photograph of three things; an analogue photograph image, a mirror image of the photographer a 'split second' before the taking of the photograph, and the phone camera’s view of the photographic scene another 'split second' before that. That view is of the analogue photograph plus a yet earlier reflected view of the photographer about to take the photograph plus a yet earlier camera view of the photograph about to be taken...
(Got sick of trying to get this any better by hand... too many jelly-like degrees of freedom to control. Every tiny displacement of the phone camera 'echoes' or ripples down the time tunnel.)
Then and now. Tempus does indeed fujit. The red eye in the colour view is from an eye procedure, not booze. The B&W just reveals I was wearing contacts. It was shot by weak indoor lamplight, about 48 years ago, when I was trying to learn what my Olympus Pen FT could do (or what I could do with it anyway), and looking for a subject for a spool-finishing shot. The half-frame was incomplete. The image is from only a quarter of a full Ilford Pan F frame. iPhone and MacBook were the other tools involved in this single image capture.
It's all a mirror image, but that looks right to me. It's what I see when I shave (which evidently I have not always done).
This is the same model as Mélisande*'s "Stars Unlimited", David made an independent discovery.
Folded from a hexagon cut of a square of 30 cm on the side of Torreón paper.
Ad infinitum, thought can bend ideas themselves as each pensive notion gets so deep that absolutes fall into the abyss. Eventually, our thoughts think thoughts of their own and the sideways spiral of ideology creates its self out of itself. Meaningless jabber or insightful reasoning worth considering as a wicked wisdom of this world. You be the judge.
Best when viewed in LIGHTBOX.
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There are all together only two models.
related ones:
www.flickr.com/photos/119967028@N08/27688564531/in/datepo...
Maybe you will like those one too :
A nine-patch of nine-patches made from a nine-patch ... the starting point is here and in the first comment.
Mosaic of my Recursive Chessboard set. See that set's description for explanations.
See also my Recursion set for other recursive subjects.
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Press "L" for Lightbox view - looks better on black!
-Strobist info: Flash Yongnuo 468 located on right side (power to 1/8). 4 40w bulbs located at the top right. A reflector on the left.
-Strobist info: Flash Yongnuo 468 situado en lateral derecho (potencia a 1/8). 4 bombillas de 40w situadas arriba a la derecha. Un reflector situado a la izquierda.
From an octagon previously painted with acrylics.
Diagrams in Origami Bogota convention book "Páginas de Origami 2024".
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From an octagon of Tant paper.
An attempt to turn a modified version of the Keller twist into a flower-tower recursive thingy.
A dead end, actually, the second twist is different, no opportunity to get a third one.
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Just a simple Julia recursive-spreading design.
Exper - www.hobosedizioni.it
Designed using: Apophysis - Rendered using: Flam3
Life of a construction pit project (additional description in album - Tobacna: Life of a construction pit)
Mamiya 645 Pro TL, Kodak Ektar 100
Ljubljana, February 2018.
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How many units does this have?
Well, I didn't bother keeping an exact count during assembly, but the way I saw it, there were still at least three ways to calculate this quantity.
By coloring pattern. This only required keeping track of the number of units in a particular section of the cube, which was much simpler than keeping track of the total number of units used so far. There were by my count three (mutually perpendicular) sets of 80 red, 96 dark orange, 80 light orange, 64 dull yellow, 64 saturated yellow, 64 light green, 80 dark green, 96 light blue, and 80 purple units. That came out to 3 * 704 = 2,112 units.
By face count. Once you know how many squares are on the outer surface of the object, multiply by 4 (the number of edges per square) to get the number of edges, then divide by 2 since every square shares an edge with its neighbor. That will give you the number of edge modules needed for the polyhedron.
There are 20 level 1 Menger sponges in this thing; each level 1 sponge has 4 * 6 = 24 "internal squares" and potentially up to six "external faces", each consisting of eight squares ringed around a central hole. Furthermore, of those 20 component sponges, the 8 "corners" expose only 3 "external faces", while the other 12 expose 4 "external faces". (20 * 24) + (8 * (3 * 8) + 12 * (4 * 8)) = 1,056 surface squares. 1,056 * 4 / 2 = 2,112 units.
By recurrence relation. Obviously, Count(0) is 12, Count(1) is 144, and Count(2) is 2,112. I tried several times to determine a recursive equation for Count(n) given Count(n-1), but each time, the formula I came up with was found wanting for one reason or another. Ostensibly, once a suitable recurrence is found, I can use Wolfram Alpha to derive a closed expression solely in terms of n for the number of edges in a level n Menger Sponge. That's what I really want, but I'll leave that work to others.
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