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Published: Tue, 20 Feb 2018 06:45:41 UTC

Last Build Date: Tue, 20 Feb 2018 06:45:41 UTC

 



Inceptionism

Tue, 23 Jun 2015 00:00:00 +0000

June 23rd 2015 Inceptionism Artificial neuron network are algorithms mimicking the behavior and interactions of neurons. They can be trained to distinguish classes of stimuli, a feature used for instance in the domain of image recognition. A large number of images of the same type of object are presented to the neuron network, which gradually encodes the "essence" of the visual features of the object. The precise way in which these features are encoded into the network are however hard to understand, as the learning process is automatic. A team at Google managed to visualize the "mental image" that a neuron network has of the object it is supposed to recognize. For that, they started from random images or photographs and made the neural network enhances the features of the images that it would tend to recognize. This results in strangely surrealistic and sometimes fractal pictures. The details can be found in this post of the Google research blog, the associated online gallery is here. Among my favorites are the dreamy fractal landscapes below, constructed using random images are seeds. Check also the associated video. Alexander Mordvintsev, Christopher Olah and Mike Tyka, Iterative Places 205 GoogLeNet 14 (2015), digital image. Alexander Mordvintsev, Christopher Olah and Mike Tyka, Iterative Places 205 GoogLeNet 16 (2015), digital image. Alexander Mordvintsev, Christopher Olah and Mike Tyka, Iterative Places 205 GoogLeNet 18 (2015), digital image. [...]



Exhibit

Sun, 26 Apr 2015 00:00:00 +0000

April 26th 2015

Exhibit

I will have works on display in a collective exhibition from May 1st to May 24th at Galerie Les 3 Soleils in Epesses, Switzerland. Opening on Thursday April 30th, 17h. Here are some of the works that will be shown.

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20130504-1, unique archival pigment print, 70cm x 70cm.


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20130610-1, unique archival pigment print, 70cm x 70cm.


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20110121-5 "Fractal Mondrian", unique archival pigment print, 70cm x 70cm.


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20140228-1, unique archival pigment print, 50cm x 50cm.


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20140329-1, unique archival pigment print, 50cm x 50cm.




Earth View

Sun, 14 Dec 2014 00:00:00 +0000

December 14th 2014

Earth View

The earth's crust displays some very nice fractal patterns that can be spied on Google Maps, as featured in previous posts Geological artwork, Ashes and ice, Sahara fractals.

There is now an extension for Chrome, Earth View, that features a pretty satelite image each time you open a new tab. You can click on the bottom right to open a Google Map tab and explore the area. Not the best for productivity, but awesome to discover interesting places.

src="https://www.google.com/maps/embed?pb=!1m13!1m11!1m3!1d121820.0049553391!2d25.29378480160818!3d23.63600259189505!2m2!1f0!2f0!3m2!1i1024!2i768!4f13.1!5e1!3m2!1sen!2s!4v1418594861457" width="500" height="500" frameborder="0" style="border:0">

src="https://www.google.com/maps/embed?pb=!1m13!1m11!1m3!1d17636.787455335296!2d11.260469628908593!3d16.012931950948236!2m2!1f0!2f0!3m2!1i1024!2i768!4f13.1!5e1!3m2!1sen!2s!4v1418594948371" width="500" height="500" frameborder="0" style="border:0">

src="https://www.google.com/maps/embed?pb=!1m13!1m11!1m3!1d228511.19703618786!2d25.29996171116376!3d24.509315678786!2m2!1f0!2f0!3m2!1i1024!2i768!4f13.1!5e1!3m2!1sen!2s!4v1418595030154" width="500" height="500" frameborder="0" style="border:0">



Iterations

Sun, 05 Oct 2014 00:00:00 +0000

October 5th 2014

Iterations

All my recent works are obtained by iterating rational maps of the Riemann sphere to itself that have dense chaotic orbits. Each point on the sphere corresponds to an orbit, and is essentially colored according to the mean distance of the orbit to a given point on the sphere. Because of the dense chaotic orbits, dense fractal patterns appear in this way. Related patterns appear when one considers iterations of the original map. One can picture the nth iteration of the map by taking into account only every nth point in the orbit when computing the average distance of the orbit. The resulting patterns are closely related, their structures disintegrating slowly as n is increased.

The following series of works exemplifies this phenomenon. The rational map is a Nova map with exponent 4. The images depict respectively the 1st, 4th, 6th, 8th and 12th iteration of the Nova map. Click on the pictures to get to the page of the work, where you can either zoom into the picture, or see the whole spherical pattern panoramically.

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20140905-1. A dense Nova Julia set, first iteration.



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20140906-1. A dense Nova Julia set, fourth iteration.



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20140907-1. A dense Nova Julia set, sixth iteration.



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20140908-1. A dense Nova Julia set, eighth iteration.



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20140909-1. A dense Nova Julia set, twelfth iteration.




Frank Berg

Sun, 24 Aug 2014 00:00:00 +0000

August 24th 2014

Frank Berg

Some interesting generative works by Frank Berg. You can see a few more on his flickr account.

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Frank Berg, System5_12Msp02 (2007), digital image.



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Frank Berg, System5_12Msp (2007), digital image.



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Frank Berg, System5_12vor03 (2007), digital image.



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Frank Berg, System5_10vor01 (2007), digital image.




Bridges 2014

Wed, 13 Aug 2014 00:00:00 +0000

August 13th 2014

Bridges 2014

The 2014 Bridges conference on Arts and Mathematics is starting tomorrow (August 14th) in Seoul. The following three works of mine will be on display in the art exhibition. All three of them feature the same dense Julia set of a Lattès map. An orbit of the Lattès map is associated to each pixel, which is colored according to the mean distance of the orbit to a reference point of the Riemann sphere (see this blog post for more details). The pictures look different only because different reference points have been picked for each of them.

You can see the full list of works on display here.



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20120514-1. A dense Julia set constructed from iterations of the following Lattès map: z -> (z3+a)/(az3+1), with a = exp(2pi/3).



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20120526-1. A dense Julia set constructed from iterations of the following Lattès map: z -> (z3+a)/(az3+1), with a = exp(2pi/3).



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20120601-1. A dense Julia set constructed from iterations of the following Lattès map: z -> (z3+a)/(az3+1), with a = exp(2pi/3)




High ball stepper

Wed, 09 Apr 2014 00:00:00 +0000

April 9th 2014

High Ball Stepper

The music video of "High Ball Stepper" by Jack White is a great example of "analog generative art", namely the use of physics laws to create artworks. A short list of some of the physical effects involved can be found here.

This video was spotted on this very interesting tumblr blog about fluid dynamics.

width="500" height="281" src="//www.youtube.com/embed/sRbnAxrS3EM" frameborder="0" allowfullscreen>



Appolonian gaskets

Sun, 30 Mar 2014 00:00:00 +0000

March 30th 2014

Recursive Appolonian gaskets

Francesco de Comité has a very interesting set featuring recursive Apolonian gaskets. As far as I can guess, these pictures are created as follows.

Apolonian gaskets are fractal coverings of a disk by disks of smaller sizes. The images of fdecomite are created by filling the disks of an Apolonian gasket by Apolonian gaskets, and iterating the procedure. As there are different types of gaskets, one can combine them in many ways (including possible rotations at each iteration) and obtain a great variety of dense fractal patterns. For instance, a few Sierpinski triangles lurk in the images below.

[Update:] A short paper describing the algorithm is available here.

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fdecomite, Verifying4 (2013), digital image.



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fdecomite, Snowflakes (2012), digital image.



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fdecomite, Filling by circles (2012), digital image.




Michael Faber

Sun, 02 Mar 2014 00:00:00 +0000

March 2nd 2014

Michael Faber

David Makin asked me to advertise the International Fractal Symposium, which can be of interest to some readers of this blog. It will be held in San Sebastian, Spain, from June 25th to 27th. You can find all the details here:
http://www.mathartistry.com/
Unfortunately, I will not be able to attend.

Below, some very interesting dense IFS fractals by Michael Faber. Don't miss his deviantart gallery. Click on the images below to get full resolution pictures.

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Michael Faber, Puzzle (2012), digital image.



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Michael Faber, Pinch (2012), digital image.



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Michael Faber, Dragon Storm (2012), digital image.




New panorama applet

Sun, 23 Feb 2014 00:00:00 +0000

February 23rd 2014

New panorama applet

Many of the dense fractals pictured on this website naturally live on a 2d sphere. A while ago, I started displaying them as full spherical panoramas using a Java applet (see this blog post). With all the recent problems with Java, and browsers strongly discouraging people to launch unsigned Java applets, I had to find another way of displaying them. Luckily, Matthew Petroff wrote a very nice WebGL applet for this purpose, Pannellum, which is now used throughout this website. The full collection of images coming with spherical panoramas can be found here!

A few of them are displayed below. Use the full screen button on the bottom right.

title="pannellum panorama viewer" width="500" height="500" webkitAllowFullScreen mozallowfullscreen allowFullScreen style="border-style:none;" id="pannellum_TuoiVNbAd1" src="../sphere/pannellum-src/pannellum.htm?panorama=../ 20130504-cmam13-equirect.jpg&title=20130504&author=Samuel%20Monnier&autoload=yes">

A spherical panorama of 20130504.

title="pannellum panorama viewer" width="500" height="500" webkitAllowFullScreen mozallowfullscreen allowFullScreen style="border-style:none;" id="pannellum_TuoiVNbAd1" src="../sphere/pannellum-src/pannellum.htm?panorama=../ 20120303-equirect.jpg&title=20120303&author=Samuel%20Monnier">

A spherical panorama of 20120303.

title="pannellum panorama viewer" width="500" height="500" webkitAllowFullScreen mozallowfullscreen allowFullScreen style="border-style:none;" id="pannellum_TuoiVNbAd1" src="../sphere/pannellum-src/pannellum.htm?panorama=../ 20111108-equirect.jpg&title=20111108&author=Samuel%20Monnier">

A spherical panorama of 20111108.