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A fractal is generally "a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole," a property called self-similarity. The term was coined by Benoît Mandelbrot in 1975 and was derived from the Latin fractus meaning "broken" or "fractured."
A fractal often has the following features:
- It has a fine structure at arbitrarily small scales.
- It is too irregular to be easily described in traditional Euclidean geometric language.
- It is self-similar (at least approximately or stochastically).
- It has a Hausdorff dimension which is greater than its topological dimension (although this requirement is not met by space-filling curves such as the Hilbert curve).
- It has a simple and recursive definition.
Because they appear similar at all levels of magnification, fractals are often considered to be infinitely complex (in informal terms). Natural objects that approximate fractals to a degree include clouds, mountain ranges, lightning bolts, coastlines, and snow flakes. However, not all self-similar objects are fractals—for example, the real line (a straight Euclidean line) is formally self-similar but fails to have other fractal characteristics.
Approximate fractals are easily found in nature. These objects display self-similar structure over an extended, but finite, scale range. Examples include clouds, snow flakes, crystals, mountain ranges, lightning, river networks, cauliflower or broccoli, and systems of blood vessels and pulmonary vessels. Coastlines may be loosely considered fractal in nature.
Trees and ferns are fractal in nature and can be modeled on a computer by using a recursive algorithm. This recursive nature is obvious in these examples — a branch from a tree or a frond from a fern is a miniature replica of the whole: not identical, but similar in nature.
(Taken from Wikipedia and with thanks to Licht~~~~ for the title and thought)
My first front page!
the advertising is actually for the company that makes these trucks, for... advertising. how grotesquely recursive of them
It's been a while since I uploaded any of my mosaic portraits, or blended portraits, so I thought I'd give a little poek of what I've been working on. One very good friend from long ago, a dear friend and current roommate, and of course, my indefatigable nieces.
Recursive model from a triangle.
Diagram in The Paper issue 134.
It looks like the pyramids our Federal Topographic Bureau installed on the mountains to help for measurements.
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Ni soy hipster, ni me gusta el reggaeton.
- Lío 2.0: Reto 2.0 - 29. Cápsula del tiempo.
- FlickrFridays: #226 Shot From Above
#FlickrFridays
#Shot From Above
Esta semana en el grupo Lío 2.0 el tema es muy divertido, se trata de hacer una foto que cuando la mires dentro de 20 años te traiga a los tiempos que vivimos. Yo he elegido dos formas de representar "mi momento" actual.
La primera basada en lo que parece una moda pasajera, pero que ya empieza a durar más de lo que muchos le auguraban; barbas largas, camisas a cuadros, gafas u otros objetos retro, pero a la vez lo último en tecnología.
Un verdadero hipster nunca reconocerá que lo es, pero cuidará su aspecto llevando barba bien cuidada, se rodeará de dispositivos Apple, disfrutará usando una máquina de escribir o una Polaroid, pero luego digtalizará sus fotos para subirlas a la red, jajaja...
En la otra forma de marcar 2017 se encuentra un single que hará historia como tantos otros que te percutan el cerebro cada vez que lo oyes y desafortunadamente, si no te gusta, lo oirás por todas partes y a todas horas, el "Despacito" de Luis Fonsi, me persigue y no puedo con él...
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Nikon D500
Nikkor 24-70 mm f/2.8 E ED AF-S VR
© Todos los derechos reservados. Por favor, no use esta imagen en su web, blogs u otros medios sin mi permiso explícito.
© All rights reserved. Please do not use this image on websites, blogs or other media without my explicit permission.
© Tous droits réservés. S.V.P ne pas utiliser cette photo sur un
site web, blog ou tout autre média sans ma permission explicite.
-- inspired by the title of a novel by Karen Jane Fowler
And then there's -- “In the end, we self-perceiving, self-inventing, locked-in mirages are little miracles of self-reference.”
{ Douglas R. Hofstadter }
I Am a Strange Loop
This image is the header of my new blog -
Suburban Halfling in Virtual Paradise
Location: Home
Mindwalker Beach
Some details include:
-Body, hands and feet by The Mesh Body Project (free in beta)
Skin on my head - Izzie's
-Hair by Truth
-Outfit by Tee*fy
-Jewelry by Maxi Gossamer
-Glasses by December
-Awesome sauce new boat sand box by BoOgErS for FLF
-Gardening gnome- Mutresse
-Lotus head fish and sea monster by +Half-Deer+
Sand castle - Cheeky Pea
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been looking to create one of these for some time, finally found the software - and it's free!
Downloaded GIMP and discovered there were other filters online, one called 'Mathmap' and one of the effects is this one called 'Droste' (after the Dutch company who first used this repeating motif in one of their advertisements).
Don't ask me how it works, I haven't got the foggiest!
This is what Wikipedia says about Droste:
'The Droste effect is a specific kind of recursive picture, one that in heraldry is termed mise en abyme. An image exhibiting the Droste effect depicts a smaller version of itself in a place where a similar picture would realistically be expected to appear. This smaller version then depicts an even smaller version of itself in the same place, and so on. Only in theory could this go on forever; practically, it continues only as long as the resolution of the picture allows, which is relatively short, since each iteration exponentially reduces the picture's size. It is a visual example of a strange loop, a self-referential system of instancing which is the cornerstone of fractal geometry.'
I found out that Shuzo Fujimoto’s molecule used in his CFW 91 star, can be changed into a fractal. By pulling some paper outside in the center, you can get a small hexagon from which a smaller copy of the original star can be folded, and the process can continue for as many times as the paper and folding precision allow. Just like the plain star (which can be considered a level-1 fractal), versions with more levels can be tessellated.
I’m not sure if Fujimoto was aware of this possibility: on one hand, I haven’t found it published in any of his books, but on the other, he did publish the design I call Lucky Star Fractal which is based on a similar idea, and if I noticed the possibility of fractalizing CFW 91, so may have Fujimoto himself.
See origami.kosmulski.org/models/fractalized-cfw-91 for a version with moe pictures and links.
If you are a fan of my work, I would really appreciate it if you would "like" my page on facebook at: Josh Sommers Art. Thank you!
A long overdue droste version of my drawing hands image. I don't know why I didn't think of it sooner!
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Please come bringing new things.
Let very old things come into your hands.
Let what you do not know come into your eyes.
Let desert sand harden your feet.
Let the arch of your feet be the mountains.
Let the paths of your fingertips be your maps
And the ways you go be the lines of your palms.
Let there be deep snow in your inbreathing
And your outbreath be the shining of ice.
May your mouth contain the shapes of strange words.
May you smell food cooking you have not eaten.
May the spring of a foreign river be your navel.
May your soul be at home where there are no houses.
Walk carefully, well-loved one,
Walk mindfully, well-loved one,
Walk fearlessly, well-loved one.
Return with us, return to us,
Be always coming home."
-- Ursula Le Guin --
Always Coming Home
A collage postcard to 'home'...
Earthchild's pose by LouLou Teichmann of Bauhaus Movement
Wearing: Mesh Body Project, Izzie's, Miamai, Wasabi Pills, Maxi Gossamer, Lassitude & Ennui, Schadenfreude
Pose for the homeward bound avatar by Mien
Wearing: Glam Affair, Truth, SLink, Spirit Store, and more...
Earth for both avatars by Mesh Mafia
Multiple backgrounds for collage from Hubble telescope photography and elsewhere...
Both avatar photos taken in Second Life
Great story about these stripes by their creator...
giam.typepad.com/the_branding_of_polaroid_/2004/07/polaro...
I have had many people ask me about purchasing prints. I would like to accommodate these requests in an easy, straightforward way so I have placed a PayPal button here that you can click on and purchase a print. I will send out a 5x7 on photographic paper and the price includes shipping. I am asking $30. This is not the original Polaroid. Please include the title of the print so that I know which one you want. Thanks,
Grant
Looking down the Landmark Center's old marble stair case kinda gave me the willies.
Got more willies when I found out: John Dillinger's girlfriend (Evelyn Frechette) and Public Enemy Number 1, Alvin 'Creepy' Karpis (escorted by J. Edgar Hoover himself) were tried in this building and walked up these stairs to the 3rd floor courtroom. Evelyn got 2 years for harboring Dillinger and Mr. Creepy got life for kidnaping beer man William Hamm.
Design by Ben Goldberg. I saw a photo of this from Jorge Jaramillo, who said there is a creasepattern or something available on the designer’s facebook page. I don’t do fb much these days, so I figured it out using Jorge’s photo.
Three layers is as much as I want to do from 15cm kami... I probably could have gotten a fourth layer in, but it wouldn’t have been pretty.
At work :)
Build made with Bricklink Studio 2.0 with existing parts and image enhanced and edited in Photoshop.
Male downy woodpecker photo made from repetitions of the same photo
Created with www.dumpr.net - fun with your photos
Acrylic on wood panel ~ 18" x 24"
237 hours - 30 sessions
"The Micronaut"
This painting illustrates my continued interest in the "Underworlds" where tiny universes exist beyond our senses, and my fascination with a possible future where man utilizes technology to evolve beyond our current state. This piece brings those two ideas together for me.
I envision a future where mankind has reinvented itself through 'self evolution'. Some day you will be able to 'be' anything we can imagine. Not only will we live indefinitely, we will be able to take any form we wish, and live a multitude of lives limited only by our imaginations.
This may not be so far out! When we hit the "Technological singularity", (an "intelligence explosion", suggesting that if machines could even slightly surpass human intellect, they could improve their own designs in ways unforeseen by their designers, and thus recursively augment themselves into far greater intelligences. The first such improvements might be small, but as the machine became more intelligent it would become better at becoming more intelligent, which could lead to a cascade of self-improvements and a sudden surge to superintelligence (or a singularity).) we will, by using the machines yet to be invented, be able to speed up, and control the path of human evolution. We will develop into a new 'post human' form.
This painting is one of many visions I have of the future. A blind boy* has invented a "bio-vehicle" (a living machine) to take him through a microbic universe.
*(Yes!, of course he could cure his own blindness … He's probably just got his eyeballs in the shop for the latest upgrade!)
Cross view this photo to see the 3D.
Step 1 - Cross your eyes until you see 4 images instead of 2.
Step 2 - Then relax your view so the images move together and you see only 3 images.
Step 3 - When you see 3 images stop changing your focus - see the center image is 3D.
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This is fun...
Not perfect but a good start, you'll spot the flaw fairly quickly I think...
Do you know what the flaw is?
The image is made possible by magic computer code written and freely shared by Pisco Bandito. I highly recommend you visit his fantastic photo stream.
Have you ever wondered what part of you is really you? I mean, we all are the sum of various influences (parents, brothers, sisters, friends, wife, husband, kids, colleagues, etc.), and of various experiences (most of which we did not choose in the first place), but does some kind of personal core exist? Is there something inside you that is purely your own being? And if so, would it even be possible to identify it, to store it in some way, to clone it or transmit it?
I was day dreaming about that, when the idea of this recursive image appeared in my mind. I thought a steampunk environment would fit the project nicely. As usual, I started by drawing some rough sketches, which proved to be very useful here (preparing the appropriate position in order for the multiple photos to align well was important). Then I disguised myself with a hat and goggles I've bought a long time ago (for another project that I've never finished), and shot a self portrait as well as all the other items: flame, copper tubes, steam, and so on. The editing part was fun, because I was unsure of the result until the very last steps: I spent 90% of the time on the main character, and all the other copies were created at the end. It felt a bit like a little surprise ;-) Thanks for watching!
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This is the public telephone box on Surrey Street in Sheffield. The droste effect was created using PhotoSpiralysis and the source image was a panorama of four rows of four portrait frames, stitched using PTGui.
Camera: Canon EOS 90D
Lens: Canon EF-S 17-55mm f/2.8 IS USM @ 55mm
f/9
0.6s | 1/6s | 1/25s (+2/0/-2EV)
ISO100
Just that. Early attempt at PS background here. Not strictly a Droste or recursive photo, but it's my take on a photograph within a photograph.
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Any download, copy, duplication, edition, modification,
printing, or resale is stricly prohibited.
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Another take on the recursive scream concept. Playing with lighting, HDR, Orton and self photography. This one inspired by Aliens.
... or, rather, gimme 85!
Either a climbers dream (this microhold suddenly feels like a jug) or nightmare (how am I supposed to coordinate all those fingers?).
Inspired by seanhepburn2006 , I just went a few steps further.
Strobist Info:
Umbrella from above.
And a little bit PS (I don't really have 85 fingers).
Hints and fair comments are always appreciated.
Don't use this image on any media without my permission.
© All rights reserved by Christian Staack.
Bending Light #78
For new viewers: these 'Refractographs' are analogue images of the refraction patterns of a single beam of light passing through various transparent objects. This is a double refraction or recursive pattern - it is formed by passing the refraction pattern of one of my coloured plastic creations through a piece of glassware to make another, more complex pattern.The image is captured directly on to 35mm film, no camera lens is used ( this is a photogram using film instead of photographic paper), the transparent object replaces the lens. The tangled fragmented background consists of complex diffraction patterns. This is an analogue image and has not been computer generated.
The sign is comical in itself: stick figure hits his head on overhanging sign. Beware!
But this is a SIGN ABOUT THE SIGN. The logic behind its existence escapes me: without the sign there, there would be no need to warn about it.
W
T
F?!?
(Pic taken while going down the escalator opposite. Original story here.)
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This is a recursive version of the Lucky Star molecule. Just like the non-recursive version, it can be tessellated or used for decorating a box. The back of this model when folded standalone rather than tessellated can either be closed or it can be opened and some extra flaps folded up which results in a pattern resembling a flower.
Despite this not being the first time around this model is invented (see below), I’m really happy with it. The collapse is rather difficult at first, but with some practice it becomes quite pleasant, especially if you only fold up to level 3 (the one in the picture is level 5, folded from a 35 cm sheet of Edokosome paper). The scaling factor is sqrt(3) which means that the levels shrink quite rapidly and a large sheet is needed to go many levels deep. After 4 iterations, this molecule is reduced by a factor of 9, compared to just a factor of 4 for the Hydrangea whose scaling factor is sqrt(2). Also, due to this model’s construction, folding levels deeper than 3 requires reaching through multiple already collapsed layers which is difficult and night-impossible without the help of a folding tool. However, a level 3 Lucky Star Fractal can be folded from a hexagon cut from an A4 sheet and it is quite quick to fold, compared to many of my other models. I rarely fold a model more than once, but the level 3 version of this star I have folded many times over since it makes a nice decoration and after some learning, is a real pleasure to fold.
While I came up with this design myself, due to some research I perfomed after designing the regular Lucky Star, I learned that others have designed the same model before me. Haligami (Halina Rościszewska-Narloch) played with a recursive version of her Day and Night Tessellation, which is almost exactly the same model as this one (only the locking of the rays in the last level is different). Shuzo Fujimoto designed this model even earlier - I was able to identify it thanks to some pictures posted by Eric Gjerde who reproduced the model based on a CP found in a book. We don’t know what name Fujimoto used — Gjerde used the name Logarithmic Star.
There are also a number of models which differ from this one, but still exhibit a number of similarities, either in the look of the finished model or in the way it is constructed. Melisande designed Star Unlimited a la Fujimoto which looks the same on the front side but has a different back and a different CP. The general construction is similar to Blooming Fractal Flower by Joanna Sobczyk. In the open-back variant, the back side resembles Floral Perpetua by Dasa Severova.