Mobius Transformations video (A YouTube hit)

From our friend Andrée at meeyauw:

An informative and beautifully produced YouTube mathematics hit. There is a YouTube link, where you will find a link to the original source of the video. You can download the video to your own drive. You really should watch this, even if you don't like math (gasp).

Well, we at CatSynth of course love mathematics, and appreciated this video. It is about Möbius transformations, an important concept involving complex numbers and geometry. You can watch the video below:

Science, light and cats

A few scientific articles that made the popular press this weekend also piqued our interest here at CatSynth. They both involve electromagnetic phenomenon – which in our daily world is most commonly observed as light.

So here's a story about light and cats, or rather a cat engineered to glow in the dark:

South Korean scientists have cloned cats that glow red when exposed to ultraviolet rays, an achievement that could help develop cures for human genetic diseases, the Science and Technology Ministry said.

Three Turkish Angora cats were born in January and February through cloning with a gene that produces a red fluorescent protein that makes them glow in dark.

You can read the whole article here. It is quite interesting, though we at CatSynth are not so sure about genetically modified cat concept.

We now move from glow-in-the-dark cats to the field of quantum computing, in which quantum states of electrons are used to store computational values (much like semiconductors are used in conventional computers). From the folks at ZDNet Australia:

Researchers from the University of Queensland have taken a significant step in the quest to build a quantum computer, creating a light-based quantum circuit capable of basic calculations and moving quantum computing closer to a becoming a reality.

Theoretically, quantum computers leave even today's most powerful conventional supercomputers in the dust. It has also been long known that hypothetical large scale quantum computers could find the prime roots of large composite numbers, allowing them to “crack” modern data encryption.

This additional computing power is a result of the quantum bits, or “qubits”, upon which quantum computing is based. Qubits are special bits that use the quantum properties of subatomic particles to make calculations. Quantum computers take advantage of a special quantum property called “superposition”, allowing one quantum computer bit to act as many.

Pretty hard core, but those interested are encouraged to read the full article, and maybe a bit more about quantum computing.

Cats of course have a famous history in quantum physics as well…

New Podcast: "Bi-fur-cation" demo

Click here to listen or subscribe.

Some might consider tonight's podcast a “rerun” of sorts, as this musical example was featured in the CatSynth article The Logistic Function and its Discontents. This is actually one of our most popular articles of our stats/records are to be trusted, combining mathematics, the work of Antoni Gaudí, and some of my favorite electronic-music techniques. Those who have not read the article are encouraged to do so – I hope to post a follow-up one of these days. Or you can just listen to the podcast as a musical curiousity.

CatSynth 1st Anniversary

Today we celebrate CatSynth's first anniversary.

It's been one year since we posted this photo on July 19, 2006:

The idea came from a friend who said something like “dude, you should do a website about cats and synths.” So I did. Really didn't have too much idea what I would write about. I quickly learned that there was quite an abundance of pictures of cats and synths, and sites like matrixsynth had been collecting such images for a while. Indeed, one of the first external “CatSynth pics” to be posted here was of matrix's own cat JD:

Sadly, we recently learned that JD passed away this month. We offer matrix our sympathies. It's always sad to hear about cat friends passing away (or human friends, for that matter), and we at CatSynth have seen our share this past year.

I expect to post more this evening reviewing the year with photos, not-so-useful stats and the other things we at CatSynth like to think we do well…

CatSynth pic: lissajous (chaos link)

Via matrixsynth:

Originally from gerald:

My cat loves the Lissajous this thing generates

So what is a “Lissajous”? it is actually short for Lissajous curves or Lissajous figures, a class of 2D (and 3D) curves describing complex harmonic functions, or more simply multi-dimensional sine curves. The following equations describe a general Lissajous curve on an x-y coordinate plane:

x = A sin(at + φ)
y = B sin(bt)

Most of the time, one leaves out the A and B, which case all the curves fall on a convenient unit square.

The most commonly described Lissajous curves set the phase term φ to π/2, i.e., a standard cosine function, and have a and b at integer ratios, like 1:2, 6:5, etc. You can think of these as natural harmonics, like in musical sounds. You can see a few of the graphs below, first for a=1 and b=2:

Here are 3:2 (a:b), and 9:8, respectively:

As you can see, the higher the ratio, the more complex and dense the figure. If you add all the figures up together, you should be able to fill the entire unit square.

There are all sorts of interesting special cases. For example, if you set a and b equal, you will get a circle. If you additionally set the φ to zero, you will get a straight line. Finally, you can mess with different values of φ, like 0.3 in the first drawing below, or set a and b to non-integer values, to get all sorts of interesting variations:

It is interesting to think about these sorts of functions by relating them both visually and aurally (i.e., synthesizing the corresponding waveforms), but we will leave that as an exercise for interested readers, perhaps returning to the topic in a future article.

Trying a little experiment. Trackposted to Gone Hollywood, Conservative Cat, The Crazy Rants of Samantha Burns, and The Pet Haven Blog, thanks to Linkfest Haven Deluxe. The links here and in the trackbacks do not necessarily reflect the opinions of this site or its contributors.


I needed some intellectual diversions over the last couple of days, and last night I took another look at concept of software art that has intruiged me recently.

Fluxus is a system for live software art that combines programming with audio, visual and interactive elements. It comes to us from the same people who made Quagmire, in which programs ran inside of monochrome images.

Some interesting statements from the Fluxus website:

act of a flowing; a continuous moving on or passing by, as of a flowing stream; a continuous succession of changes

On a more technical level:

Fluxus reads live audio or OSC network messages which can be used as a source of animation data for realtime performances or installations. Keyboard or mouse input can also be read for simple games development, and a physics engine is included for realtime simulations of rigid body dynamics.

The use of OSC is of particular interest, as such a system becomes an interesting companion to Open Sound World. It also rekindles my idea of providing an OSC-based livecoding environment for OSW.

Unforunately, I have had some difficulty getting it installed (or compiled) for Mac OSX, so I haven't been able to do much myself. Hopefully I will be able to get that working soon…


No, not that quagmire!

Rather, I am talking about an interesting software art project in which programs exist within a bitmap. From the author:

Quagmire is an emulation of an impossible 8bit processor, where all memory is addressed in 2 dimensions, and is represented by pixel value. Program execution threads can run up, down, left or right. Sections of code are visible in memory, as are the processes as they run. Unlike a normal computer the internal process of the machine is visible. Programs are drawings.

The programs are executed by scanning pixels in the bitmap/drawing and interpreting them as instructions that can change the original bitmap, including the parts that are being “run.”

The best way to illustrate this concept is will an illustration, or rather, a series of illustrations:

In the above example, the “program” in the lower-left corner switches various pixels on and off, and spawns more copies of itself in the process. After running for a while, one ends up with four animated “stripes” of execution.

The program changes dramatically if the “non-executed” area of the image is different. For example, we can paste my “digital fish” logo onto the image and then run the program again:

The very orderly execution over the empty image becomes much more complex in the presence of the fish logo.

Although the complex changes in the image can seem random, they are completely deterministic. Running the same program/image in Quagmire yields the same result every time. Indeed, this can be seen as an example of chaos in which simple processes can produce incredibly complex results that may seem random but are completely deterministic.

Some images produce less complexity. Applying the same program to a picture of Space Ghost (who has appeared in several posts on this forum recently) causes a small number of changes after which the program comes to a halt:

By contrast, applying the program code to an image of Luna appears to grow ever more noisy and complex:

The Quagmire site has more detailed technical information about the programming language (more of a machine language) and an implementation in which you can run your own programs. You can also find links to more examples of “software art.”

It would be interesting to explore software art that uses audio in addition to (or instead of) visual images…

Worthless Kitty Interlude: 1990 and 2041

I was listening to the radio last night on the way home, and the program host was referring to an event 17 years ago, in 1990. Some thoughts:

1990 is 17 years ago, or half a lifetime ago.
2007 will be half a lifetime ago in 2041.
In 2041, I will be 68 years old.

many cats can live to 17 years or more

my grandfather (on my mother's side) died at age 68 in 1982.

Fun with stats: digits in Pi

From Eve Andersson's Pi land, we have these histograms of the frequency of (base 10) digits.

The first 100 digits of pi:

0 8
1 8
2 12
3 12
4 10
5 8
6 9
7 8
8 12
9 13

Things even out pretty nicely by about 1 million digits:

0 99959
1 99757
2 100026
3 100230
4 100230
5 100359
6 99548
7 99800
8 99985
9 100106

The digits are just white noise, there might be an interesting pattern now and then, but that is to be expected statistically. Besides, these are base 10 digits, which are an arbitrary representation based on the fact that we have two hands with five fingers apiece…

I could share some more interesting facts and formulae, but printing the greek character pi on a blog is, as they say, a pain in the butt. And I am not in the mood for that tonight.