Manhattan Voronoi Tessellations

Sometimes it's nice to visualize a math problem. Visualization can provide insights and also sanity checks. This is a Manhattan Voronoi tessellation with a Gaussian density function.

Tomorrow I'm going to implement a Lloyd iteration to compute a Manhattan centroidal Voronoi tessellation. I anticipate that the resulting tessellation will be more regular and aesthetically pleasing.

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This afternoon I continued doing exercises in probability theory out of the book All of Statistics. The exercises continue to be challenging and interesting. Today I focused mainly on conditional probabilities and independence of events.

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During my walk/run today, I passed through a park on the west side of the river that I had not visited in a few weeks. The fountains were all going and there were a lot of flowers:

The weather forecast shows cool weather and rain for the next several days, so I'm glad I got out to enjoy the sunshine today. Also, managed to get in a load of laundry. Might not be able to hang clothes on the roof for a couple of days either.

Stats and feria

I continued working on learning advanced probability and statistics using All of Statistics. Today I worked through the Monty Hall problem. Moral of the story, when Monty asks you if you want to change your door choice, do it.

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I watched little Spanish Netflix before class, but still felt a little behind the curve today.

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I walked through the feria grounds today. The large scaffolding at the main entrance now has its facade:

Ready to go, only one more month until feria. A large number of the family tents are also now in place:
 

This is essentially a 9-day party with people hanging out at each other's tents getting massively wasted. Definitely not my scene, but I'm sure Laura and I will wander through it once for the mere spectacle.

Random obstructions

Yesterday I took this photo in Barcelona while waiting for the airport bus at Plaça d'Espanya:

Laura lamented the presence of the various lamp posts and traffic signals. Given the flatness of the sky, I though this was an ideal situation for some Snapseed photo editing. I loaded the above image into Snapseed and erased the various random obstructions. I also cropped it a bit and got this:

In the flat sky, they get wiped out pretty well, but you can still see the bottom parts of the posts. In more detailed parts of the photo, Snapseed doesn't work as effectively, so I usually just leave those bits alone and hope people don't notice.

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With daylight savings time resuming here in Spain over the weekend, were now back to 6 hours ahead of the east coast and 9 hours ahead of the west coast. The advancing spring and the changing sun angles make every evening along the river a little different:

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Speaking of random obstructions. Today I started coding an example algorithm I'm developing. In part of it, I need to generate random numbers according to a bi-variate density distribution. After looking around a bit on-line and getting what I thought were overly complicated solutions, I decided to take a shot at writing my own recipe. For a non-negative density function, r_values, with maximum, rmax, just do this:

Not sure if it's mathematically sound, but it does what I need.

Home again.

 One last lovely sunrise from the hotel room:

We were up and out by about 8:30am this morning. Using our trusty 48 hour transit pass, we made our way on the L4 metro line down to the airport bus stop. Shortly, we discovered that this pass doesn't work on that particular airport bus (turns out its a private operation that only seems to be public transportation). We found out, however, that there is a public transportation bus to the airport, so Laura got on her phone and navigated us to that bus stop. A few stops on the L3 and we were back near where we were yesterday when we saw all the fountains in front of the art museum. We found the "public" airport bus stop and waited. In a few minutes the bus arrived and we made it down to the airport in plenty of time--squeezing every drop of value out of our soon to expire transit pass:

We arrived in Sevilla on time and with a THUMP. Our landing in Sevilla was easily that hardest landing I've ever experienced. We also landed in pouring down rain. We made our way to the bus to get downtown and home. Not long after we got on the bus, the rain slackened. By the time we got downtown, it was barely a drizzle.

We had a quick lunch and then off to our respective language classes. I did my oral presentation on a famous American family. I talked about Lloyd, Beau and Jeff Bridges. Mostly because I like Jeff Bridges. It went well with a few useful corrections by the teacher.

After class, I went home and did a bit of cleaning. Also, Mario dropped by with the final repaired chair.

The unusually damp/cool weather certainly dampened activity in the neighborhood. The street was unusually quiet this evening:

Park Güell

Today the main event was a visit/tour of Park Güell. This Gaudi designed park was started by Eusebi Güell as essentially a private housing development centered around a park. This "get back to nature" approach was a good fit for Gaudi. The effort started in 1900 with the development of the park and attempts to entice wealthy folks to buy/build homes in the park. As a commercial venture, it failed. The rich folks thought that the park was too far from the center of Barcelona and didn't bite. It was turned over to the city and is now a municipal park. Like la Sagrada Familia, this park is unusual and fantastic. These rough stone walkways wind through the entire grounds:

Fairy tale buildings dot the property:

One of the rough stone pillars is in the shape of a laundress:

These support pillars are modeled after tornados:

One of the buildings has been converted into the neighborhood elementary school. I can't think of a better place for kids to go to school--surrounded by Gaudi's unusual art:

This is the main entrance to the park:

After the park, we wandered down to the gothic quarter, then to the art museum (we didn't go in). This fountain in front is called "The Magic Fountain":

Further up the hill towards the art museum is the cascade fountain:

Proof that we made it to the top:

The place around the art museum was very busy because the final stage of the Tour of Catalonya had just wrapped up. Here's Chris Froome signing autographs outside of the Sky Team bus:

We went back into the gothic quarter and just like cathedrals all over the world, this one had buskers out front:

On the subway back to the hotel, or is it a bar. It's weird to see people drinking beer on the subway. That's not a thing in the US:

We went to a great little kebab place around the corner from the hotel for dinner. I'm so full. We have  a noon-ish flight back to Sevilla tomorrow.