Thursday, May 31, 2007

Directory: February through May, 2007

Directory: February through May, 2007
  • no posts in March

Monday, May 28, 2007

cascada post 14

Hommage à A.J.W. Duijvestijn

21 squares each a different size form the large square

The arrangement of squares in the picture above was discovered by A. J. W. Duijvestijn and published by him in 1978. He was a Dutch computer scientist and mathematician who lived from 1927 to 1998.

You may see a larger version of the picture by clicking on the word large in the caption under the picture.

If you would like to know the story of how 'squared squares' like the one above were discovered, comment or send me email and I will give more information in a future posting. Otherwise, just enjoy the picture.

Tuesday, May 22, 2007

cascada post 13

In the Xalapa Sculpture Garden -- Part 2

Here are more pictures of the Xalapa Sculpture Garden, taken back in July of 2005. The indoor pictures were part of a show, not part of the permanent pictures. My apologies to the artists (and to the readers) for the artists names that I did not record.

Mi nieto by Rocio Sagaon -- high temperature ceramics
(another view is in my previous Part 1 posting)

look carefully and you will see a daddy-long-legs spider

intermission -- garden flora
(photo by Esther)

made of bamboo

photo by Esther

photo by Esther

Thats all! If you want to see more, come and visit Xalapa and go to the Sculpture Garden.

Friday, May 18, 2007

cascada post 12

In the Xalapa sculpture garden -- July 2005 -- Part 1

Here are photos taken in the Xalapa sculpture garden in July, 2005. Mostly I did not record the artists names. My apologies to them. Most photos are taken by me, a few by my wife where indicated.

the entrance

Sculpture or living thing?

living thing

photo by Esther

Mi nieto by Rocio Sagaon -- high temperature ceramics
photo by Esther

detail of a wonderful cow, artist: Manuel Velázquez

Hombre Azul, by Valentina Sandoval (ceramics)

That is all for today. More coming in part 2....

Saturday, May 12, 2007

cascada post 11

Impossible Art 2

Last time I talked about the impossible art of Oscar Reutersvärd and how his first impossible drawing was a sketch he made in 1934 of a curious collection of cubes arranged like the picture at the left. Along came Sir Roger Penrose, who was three years old in 1934, and made it into a solid triangle, now called a Penrose triangle. Penrose was not yet famous (for physics, cosmology, mathematics, Penrose tilings etc) back in 1958 when he published his triangle, jointly with his father in a psychology journal. I don't have a copy of Penrose's actual picture but presumably it looked something like the triangle at the right.

In all fairness, the Penroses apparently never heard of Reutersvärd or his triangle made of cubes so it is really all right to call it a "Penrose triangle". Well, it was published in a psychology journal, and for some reason psychologists really get off on impossible figures and optical illusions and such.

Remember this? (below):

I first saw the wife/mother-in-law picture in some psychology book, probably in the 1960s.

It was only a matter of time until someone would try to make a real impossible triangle, and Bruno Ernst (real name Hans de Rijk) made one out of wood and took this photo of it in 1985.
The in-your-face spoiler is in the mirror in the background.

There is a wonderful sculpture in Perth, Australia of the impossible triangle:

Impossible Triangle by Brian MacKay and Ahmad Abas, 1999

When you walk around to the side the view is quite different:

same sculpture, different view

You can get the canonical 'impossible triangle' in scalable vector graphic format, which you can enlarge as much as you like without loss of resolution from from wikipedia. Of course to enlarge it you need an svg viewer. There is built in svg support in the firefox browser, but it was a big disappointment to me because you can neither pan nor zoom. What good is scalable vector graphics if you can't change the scale! Might as well view a gif file. Apparently a lot of folks think differently. There is a plug-in from Adobe for the IE browser that works pretty well. But you have to download and install it. The commands for pan and zoom are totally hidden and most likely the average user would never find them. Pan is 'alt + click + drag' and zoom is 'hold down ctrl and then click'. That makes it zoom in centered at the mouse pointer. Scalable vector graphics are lots of fun and easy to create. It is a shame that Adobe is dropping support for them on Jan 1, 2008. More money to be made from flash, no doubt. In any case, here is what that canonical 'impossible triangle' looks like:

canonical 'impossible triangle' converted from svg to png

And, if you didn't bother with the svg stuff but still want to see it really BIG, click on the word BIG, but if you view the big guy you may have to click on it to make the jaggies go away; that is because your browser will resize the big pic, and they don't do that very well. If it doesn't quite fit on your screen try hitting F11 to get more screen out of your browser.

Back in ancient days, when the Internet was young, most folks on the net were Unix geeks and they all had dot-sig files stored among their files under their user ids on the Unix system. These were one line text files that had to have the name '.sig'. The dot made them hidden files and the sig, I suppose, just stood for signature. In any case, whenever you posted something to the Internet the contents of your .sig file got appended to your message. There was netiquette and strong peer pressure to keep your .sig down to a SINGLE line of text. So there was this one guy named Jellby (hey I don't know his real name) and he kept posting messages with a single cryptic line of POV source code at the bottom of them. It was too tough to figure the code out and I got curiouser and curiouser till one day I cut and pasted that line of code into to the POV program and it generated this picture!

Jellby's dot-sig

If you're still here you must have figured out that I've got some kind of 'thing' for triangles, and you'd be right--but I'm thinking maybe, if you slogged through all of that, you may be just a little bit weird yourself, in a good way of course.

There is nothing special about triangles though, you can have 'impossible rectangles' too:

And somebody actually tried to build a cube like this:

But it ended up looking like this:

Possibly this inspired Escher to make this picture:

Man with cuboid--Escher 1958
Though, chances are Escher came first.

Our friend Oscar Reutersvärd:

Oscar Reutersvärd
(photographer not known to me)
also experimented with endless stairways and this was a theme in many of his drawings. The general idea is this:

endless stairway--walk downhill on bad days

This was also the inspiration for Escher's famous waterfalls picture:

Escher--Waterfalls 1961

Oscar Reutersvärd and Escher as well influenced a number of other artists, among them the Flemish-Belgian artist Jos de Mey, born 1928. Here is a painting of de Mey's with characters imitating Bruegel but with an 'impossible gateway'.

Painting of Jos de Mey's, characters after Bruegel

Here with this piece Jos de Mey satirizes a classic painting of Bruegel,

The Owl on the Gallows by Jos de Mey

namely Bruegel's 1568 painting 'Magpie on the Gallows" which,

Bruegel--The Magpie on the Gallows--1568

if we think of it as an 'impossible gallows' is surely the world's first piece of 'impossible art'.