Penrose pattern #4, 10/7/11: The Hive Mind

Title: The Hive Mind
Date: 10 July 2011
Type: Pattern
Number of tiles: 192
Color breakdown: 52 purple, 88 yellow, 52 blue
Shape breakdown: 116 kites, 76 darts
Kosher Penrose tiling rules: no

Ten on twelve for fifty two minutes.

I had the times wrong for the games on Sunday, thinking the United States and Brazil would play at noon. I was scanning espn.com to see the score for the early game and saw that Sweden had already crushed Australia 3-1 and the U.S. was ahead 1-0 against Brazil at the half. So I scooted on down to La Estrellita to watch the second half.

Walking the few blocks, I had these strange feelings. I didn't really know who I was rooting for. I wanted to see the United States get through, but I also wanted to see some flashes of brilliance from Marta, the 25 year old Brazilian superstar who is the best female player in the world right now. (The Brazilian men are in the Copa America, playing listlessly. They were behind 2-1 in the second half against the never awe inspiring Paraguayans when the Brazilian fans began the chant "We want Marta! We want Marta!", though in Portuguese of course. The Brazilian Federico Chaves Gueves took this as a personal challenge and scored the tying goal in the 89th minute.)

Well, I got both the things I wanted. The Brazilians began attacking with better passes and plays, and Marta was brought down in the box for a penalty. Both players were tugging and struggling, but the ref called it on the American Rachel Beuhler and gave her a red card.

The Brazilian coach decided Christiane should take the penalty, and that might have been a mistake. Hope Solo made a spectacular save and the Americans were still in the lead. But the ref called for do-over. The announcers didn't know why and assumed the ref had called Solo for moving off the line before the shot, but instead an American stepped into the 18 yard box a little early, which technically is infringement but in practice is rarely called.

Being a sports fan is sometimes a trip down memory lane. It felt like the famous end of the U.S.-U.S.S.R. Olympic basketball game, where the last few seconds were played several times until the Russians got a chance to win, and then it was over.

On the re-shoot, it was Marta. There was no magical save. U.S. 1, Brazil 1. The Yanks would have only ten players on the field for the last twenty two minutes of the second half, and if it was still tied, they would play one down for another half hour.

The Americans hung tough, but several calls by the ref went the other way. The game did go into extra time, and I got to see a true flash of Marta brilliance. Closely marked and at a bad angle, she toe volleyed a ball out of the air, popping it up gently into the far corner of the net where it could not be reached. Earlier on the play, the woman who passed it to Marta appeared to be offside, but there was no call. It was ten on twelve, the twelfth opponent being the ref herself. Brazil 2, U.S. 1.

And so it stayed. For a man down, the U.S, was not playing a wait and see game, but instead running hard and setting up opportunities. The game was winding down and a Brazilian player fell to the ground, hoping one guesses to use up some clock. When she was finally escorted from the field, the game went into extra time. Three minutes away from elimination.

(photo by Petr David Josek/Associated Press)
And then the miracle goal. It was not a super pretty flash of brilliance like Marta might do, it was just what a better conditioned team can do against a team who is not as well prepared. Rapinoe sent a long cross into the box for Abby Wambach, much taller than her marking player. The Brazilian goalie Andreia didn't clear it and Abby put it right on her forehead into the back of the net. 2-2 and we go to penalty kicks.

You never know when it goes to PKs, but if foreshadowing means anything, you had a very strong hunch. Hope Solo looked great all game and Andreia looked shaky several times. Hope stopped an early attempt by Diaine, who in the first half scored an own goal when trying to clear a cross, so she got to be the double goat.

(Photo by Martin Rose/Getty Images)
When it was over, the American squad was all smiles. It could be argued they will not play a team as tough as Brazil in the rest of the tournament, but this has been a very strange set of games. They play France on Wednesday and if they pull that off, they face the winner of Sweden-Japan, two good teams that are also over-achieving at the moment. The Yanks should beat the French, but in this tournament, there has been a whole lot of should that has turned into shit.

Stay tuned.

Triangles and hexagons. Simple patterns that should be better known.

Because every angle of an equilateral triangle is 60° and every regular heaxgon has angles of 120 °, the two shapes mix and match in several ways. If I use less colors than I did here, the Star of David motif in this pattern becomes much more prominent.

Here is a completely different pattern where a buffer of triangles surrounds each hexagon. This is my favorite of the regular mix and match patterns using triangles and hexagons, and I'm going to do more experimenting with color options with this one over the next few weeks.

Stunner.

To paraphrase Elvis Costello only slightly, the 2011 Women's World Cup was supposed to be "All this, but no surprises for this year's girls."

Germany was the host country. Germany had won the last two World Cups, in 2007 by not giving up a single goal. The Germans had players on their bench that would start for any other team in the world.

Japan was a challenge, but by no means an insurmountable one. It was the classic sports match-up, the big and strong German side versus the small and quick Japanese. It's always intriguing, but the smart money was all over Germany.

At the end of 90 minutes, it was still 0-0. The Germans had some bad luck when midfielder Kim Kulig fell awkwardly in the 8th minute and had to be replaced, but the big surprise was when Silvia Neid made her last substitution, it was clear that both veteran Birgit Prinz, the top goal scorer in Women's World Cup history, and Fatmire Bajramaj, the young face of German women's football, would not be used at all in this crucial game.

(Photo by Johannes Eisele, AFP)

It was still a scoreless draw after the first fifteen minutes of extra time, but in the 108th minute, the Japanese star Homare Sawa sent a perfect pass to a speeding Karina Maruyama, who put a tricky far post shot past the German goalie Angerer, who was naturally guarding the near post. This picture by Johannes Eisele captures the moment perfectly.

The emotions of the women's game are very different from the men's. There were German players weeping bitter tears and Japanese women weeping tears of joy for one the greatest successes in Japanese sports history.

The smart money said the Germans would win this thing. Pressed for a second choice, they thought the Americans had a chance, maybe the Brazilians if their suspect defense could hold together, an unlikely event given their history. As it stands now, any team that is still lacing up their boots as of today could be this year's champions, which includes the Yanks and the Samba Queens, who will meet tomorrow afternoon Pacific time.

Congratulations to the Japanese women for a well deserved and hard fought victory.

Two versions of Sierpinski's Gasket, using the new toys.

The standard version of Sierpinski's gasket is two colors. It is a simple fractal that is supposed to be created by infinite recursion, but I only have finitely many triangles, so this will have to do.

Here is a four color version of the gasket, using Pascal's triangle and mod 4 arithmetic. Four colors lets me make a bigger version, but some color will eventually be in short supply, this time it was the aquamarine.

I have an idea for how to make this using empty space as the most used shape. That should make a bigger version.

Support your local.

A logo of an oak tree has been the official mark of Oakland since 1852, but a new store called Oaklandish has redesigned the the tree to have deeper roots. The Oaklandish clothing brand has been around for about ten years, and they just opened up a new store on 1440 Broadway in Oakland, about a block away from the 12th Street BART station's exit in front of DeLauer's, my go-to place for all the supermarket rags in one convenient location, always available on Thursdays when I need them.





I went into the store last Friday and bought a few buttons, promising myself I'd buy a shirt this Thursday when I made my DeLauer's run. I am now a proud owner of an Oaklandish BART t-shirt, an very cool design that is of absolutely no use if you are trying to find your way around the bay by train.

Hey, I already know the BART map. I bought this because it looks good.

If you are an East Bay person, stop on by the store and check out the stuff. It's a good local business and it deserves your patronage.

Not according to form, more's the pity.

Through the sixteen games of the Women's World Cup being played now in Germany, predicting the winners was pretty easy work. Look at the world rankings and what ever team was ranked higher would win or at worst draw. But then came the last eight games in group play, which started yesterday and ended this afternoon, and betting on favorites based on the rankings went to hell.

The Canadians were supposed to be the sixth best team in the world and the Nigerians 27th, but after two tough losses, the gals from Canuckistan had nothing left in the tank and lost 1-0. Japan and England met in a match that would decide first and second place in their division, and England beat the higher ranked Japanese. Besides the rankings, Japan had crushed Mexico 4-0, while England had only managed a draw against las Mexicanas.

A somewhat bigger surprise, at least historically, was Australia beating the Norwegians to get into the knockout rounds. The difference in their rankings was not that big, but Norway has a much shorter trip to get to Germany and they have won a World Cup. But there was foreshadowing in the earlier games, when the Aussies fought hard against Brazil and lost only 1-0, while Norway took a 3-0 beating at the feet of the Samba Queens. The Aussies beat the Norwegian 2-1 this morning and they will be playing the Swedes this weekend in the quarterfinals.

(photo from the New York Times)

Australia is playing Sweden because the Swedes beat the heavily favored Americans. The U.S. team could have been first in their group if they had managed a draw, but they gave up two goals in the first half on a penalty and a deflected free kick and they could not manage the comeback.

This is the first time the Yanks have lost a game in group play since the Women's World Cup began 20 years ago. This picture is from the only goal they scored, when Abby Wambaugh (number 20 in white, upper left) went up for a header but the ball hit the top of her shoulder instead and went in. It's was Wambaugh's first goal of the tourney and the only bright spot in an otherwise bad day for the Americans.

So now comes Sunday, and the Americans have to face Brazil. My loyalties are completely conflicted. I love the American team, but the Brazilians are so damned pretty when it comes to putting the ball in the back of the net. The Brazilian defense is definitely suspect, but after today, the same can be said of the Yanks.

Even before these last few days of chaos, this was a tough match to predict. I usually leave prediction to the people who do it for money, but I'm going out on a limb and saying Brazil 3, United States 2 in regulation and at least one goal for the amazing Marta.

I'm definitely going to be in front of a TV for this one.