Algorithmic art

September 6th, 2008 at 0:34 · Filed Under At Home, Blogging, Mathematics · 2 Comments 

Jean-Pierre Hébert, a 68-year-old French artist, is an algorist. This is a name, proposed by Jean himself, for artists who create arts using unique computer algorithms. Apple featured Jean and his works in May 2008. You can read about him here so I am not going to repeating writing about him and his works.

When I was doing shopping alone this evening, the idea flashed in my mind. I could use Mathematica to explore algorithmic art. So, I sat down in front of my Mac and explored. Here’s my first piece of algorithmic art . It is not comparable to what Jean has done but is definitely a good start. I can’t call myself algorist yet because I created no algorithm.

The following examples are two very simple mathematics equations. The plots demonstrate that mathematics can be visualized as art.

Read more

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Butterworth low-pass filters

September 4th, 2008 at 0:14 · Filed Under At Work, Call Me a Geek, Days in My Life, Mathematics, Software Development · Comment 

I was reading about Butterworth low-pass filters since two weeks ago. Signal processing was not my favorite but this particular linear analog electronic filter had somehow captured my attention. I have interns working on some projects. One project uses Butterworth low-pass filters to process signal acquired from some sensors.

I have to verify their works using Mathematica on Mac OS X for data modeling. But there is a problem with this software. It does not have a built-in function of Butterworth low-pass filter so I need to build one.

The gain G(ω) of an n-order Butterworth low pass filter is given in terms of transfer function H(s) as:

where ωc is break frequency.

The Mathematica code with break frequency normalized at 1 rad/s:


butterworth[w1_, w2_, o_] = 1/(1 + (w1/w2)^(2*o));

LogLinearPlot[
 Evaluate[Table[
   10*Log[10, butterworth[w1, 1, order]], {order, 5}]], {w1, 0.01, 100},
  PlotRange -> {-100, 0}, PlotPoints -> 100, ImageSize -> 400]
Export["butterworth.jpg", %]
Plot of the gain of Butterworth low-pass filters of the n-order 1 through 5.

Plot of the gain of Butterworth low-pass filters of the n-order 1 through 5.

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