A-Z Challenge 19: Selfie

It’s interesting how new words come into our vocabulary, and sometimes become very popular in a short time. A selfie is a self portrait, usually taken with the digital camera on a smart phone, and usually posted instantly on the Internet, on Facebook or Instagram.

If you search for #selfie on Instagram, you get 103 million hits (I just did it). Today everybody knows what a selfie is, but who had heard this word just a few years ago?

Self portraits are not new.  Many of the greatest artists made one or more of them. Picasso, Dali, van Gogh, and Munch all painted self portraits. Making a self portrait with paint and pencil took so time (and some skills).

Making a self portrait with a digital camera is so fast and easy that nobody have the time to pronounce the full word anymore, and then we got the selfie.

Everybody are taking and posting selfies. My kids do it. Rihanna and Beyonce do it daily. Even Obama and the Prime Minister of Denmark do it (on inappropriate occasions).

I don’t post pictures of myself on the Internet, but I think I need a selfie, just to show that I’m following the trends of the time. Above is a picture I took on the chairlift a couple of days ago when I was skiing in the mountains. It shows the tips of my skis and my shadow. Does that count as a selfie?

A-Z Challenge 13: Mandelbrot set

Here’s some cool stuff for the math nerds, and a question to the art nerds. It’s about the Mandelbrot set. This is a mathematical object which was discovered more or less by chance, by the Polish mathematician Benoit Mandelbrot. What is cool about the Mandelbrot set, is that it makes some incredible pictures, using a very simple formula.

This is how you compute the Mandelbrot set: Take a number, square it, and add a constant. Repeat the procedure several times. This is the formula:

z(n+1) = z(n)*z(n) + c.

Depending on the choice of the constant c, the iterated number z(n) may stay finite, or it may grow to infinity.
There’s one more thing: Both z(n) and c have to be complex numbers, with a real part (x) and an imaginary part (y). It can be shown that if z(n+1) stays finite, it don’t get larger than 2 in magnitude. This makes the Mandelbrot set easy to compute. Just iterate the formula above (say) 50 times for all values of c (start with z(1)=c), and count how many iterations (n) are needed to make z(n+1) larger than 2. Then make a plot of the number of iterations n. Very simple. I computed the pictures below in 10-15 seconds with Matlab on my lap-top.

If you zoom on the Mandelbrot set, you will discover incredible patterns, and sometimes small Mandelbrot-set look-alikes hidden inside the full set. (To do the actual zoom, you need to re-compute inside a smaller subset of the image, to get higher resolution). The cool parts are along the rim of the Mandelbrot set.

And then comes my question to the art nerds: Is the Mandelbrot set art? It looks like art, but is it art, being created by a simple mathematical formula? What do you think?

There are fancy ways to compute the Mandelbrot set fast, and with high resolution. The code that I wrote in Matlab is not the fastest, but very simple. Here it is (lines starting with % are comments):

%-------------------------------------- 
% Plot the Mandelbrot set 
%-------------------------------------- 

%--- Set max iterations and grid size: 
nmax = 50; 
nx = 601; ny = 481; 

%--- Select a subset of the complex plane: 
xRange = [-2, 1]; yRange = [-1.2,1.2]; 
%xRange = [-1.20,-1.0]; yRange = [-0.38,-0.22]; 
%xRange = [-1.043,-1.033]; yRange = [-0.292,-0.284]; 

%--- Gridding: 
dx = diff(xRange)/(nx-1); 
dy = diff(yRange)/(ny-1); 
x = xRange(1):dx:xRange(2); 
y = yRange(1):dy:yRange(2); 

%--- Mandelbrot loop: 
for j=1:ny 
    for i=1:nx 
       c = complex(x(i),y(j)); 
       z1 = c; 
       r2 = c*conj(c); 
       n = 1; 
       while (r2<4 && n<nmax) 
          z2 = z1*z1+c; 
          r2 = z2*conj(z2);
          z1 = z2; 
          n = n+1; 
       end 
       narr(i,j) = n; 
    end 
end 

%--- Plot result: 
figure; imagesc(x,y,narr'); 
colorbar; caxis([1, nmax]); 
axis xy; axis equal;

%-----------------------------------------
% THE END
%-----------------------------------------

(The pictures where computed with the Matlab code above. the codes runs in Octave too, if you don't want to pay for a Matlab license. The white frame in the 1st picture shows the area zoomed in the 2nd picture and so on. I'm just an amateur in this branch of mathematics, known as fractals. Check out this link for a real-time zoomable Mandelbrot viewer made by the pros. )

A-Z Challenge 04: Disneyland (and Mekka)

I went to Disneyland with older boy when he was 5. I went to Euro-Disney with little boy about the same age. It’s the pilgrim trips we do with our kids.

Disneyland is Mecca for the kids.

Mecca is Disneyland for the Muslims.

But we can draw Donald Duck and Mickey Mouse without risking our lives.

(The picture above is from my archives, taken in EuroDisney some years ago. Drawings of Mohammed, by a Danish artist, can be seen here. Some of them are very good. On the 20. May 2010 was the “International everybody draw Muhammed day”. I support the initiative. Rationalism will win over stupidity in the end.) 

Scream for millions

Yesterday, the Scream by Edvard Munch was sold by Sotheby's for 120 million dollars. That's pretty expensive for a painting. I submitted my bids, but had to back out when the price passed 100 million.

I'm not sure who bought the picture.  Rumors say it was the royal family of Qatar. Whoever the buyers are, I hope they're not too disappointed when they find it's not the only Scream. Edvard Munch painted four versions of this picture between 1893 and 1910. The three other versions are owned by the Munch Museum and the National Gallery.

I f you,  like me, were outbidden in yesterday's auction, there's a consolation. In the Munch Museum, you can admire two different versions of the Scream for only $15. And they have lots of other cool Munch pictures as well >:)

(The picture above is one of the Screams owned by the Munch Museum, probably the first version from 1893. I found the picture on the Internet, for free)