X-Message-Number: 25615
From: 
Date: Mon, 24 Jan 2005 02:44:17 EST
Subject: Re: The Limpinwood X-Prize 

K-space and butterflies

From: Peter Merel <>

> The pair of butterflies took off again and did another series of 
> arabesques, loops, twists, and flings. Then they landed right back 
> where they were before. The exact same grass blades. And this in a 
> stiff breeze after a thunderstorm.

>I read that butterfly nervous systems have less than 3,000 neurons. Not 
>1 billion, like De Garis's planned "brain". Not even 75,000 like his 
>Xilinx models. Just 3,000, and most of them don't even control flight 
>muscles. But their interconnections can be mapped, if you like. It just 
>takes a microscope and some patience. Plus the willingness to undertake 
>the bad karma necessary to kill and dissect one of those little 
>beauties.

Butterfly are insects and all insects have faceted eyes. These works as 

four-waves interferometers and produce data in a so called K-space. One 
dimensional 
K-spaces are lines segment with a centered point. Data near the center 

contain mostly contrast information and more distant points are more concerned 
with 
spatial resolution. K-spaces are used for example in magnetic resonance 
scanners.

If the butterfly memorize both, the contrast and spatial complexity of its 

starting point, it has two points to recall in the K-space. To get back, it has
find a picture whose the point pair position match what it has memorized. This 
task must take less than 3 000 neurons. So, it could be indeed implemented in 
an ANN.

The next question is : why and how the butterfly get programmed with K-space 
software. The answer comes from the way 4-waves interferometers work. In one 
"snapshot" the picture definition is very bad but it improve as more snapshots 
are added. When the butterfly remains at the same place, the picture becomes 

more and more finely defined, : The resolving power get larger. When it fly and
move from instant to instant, it can't accumulate a large number of snapshots 
and the world look blurred. If it  get near its initial rest place, the 

K-space data can be partly superimposed on what it has memorized and the picture
get clearer. So it gets back to that place because it is the only one outside 
the fog.

Yvan Bozzonetti.


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