Last week I was at the beach. Whenever I go on vacation, I get hundreds of souvenirs: all my photos. Below are a few of my favorites from the trip. Our final day, we endured 35 mph sustained winds from Tropical Storm Andrea. In a house on stilts, that’s more fun than usual; the house rocked with every gust. I’m getting back around to my normal schedule, so you’ll be seeing more regular posts from me.
Alas no, I am not swimming at the shore for some time. But I like to pretend that I might be soon, and so I wistfully mull through my photos. I love to swim, and anytime I visit non-lethal water, I want in. The next best option is photographing. The two mix poorly, but I try. Below are some lovely tropical beaches, and some gloomy beaches and some extremity-numbing fjord beaches.
As a point of pride, I did get in the fjord and swim to a dock about 30 feet out, but I was going numb. Because children are insane, several children also did and wondered why I minded. This summer I’m visiting the Outer Banks of NC, and hoping to try a little surfing.
I never understood the fuss about Valentine’s Day. In elementary school, it was a day that ostracizing the odd kid was officially approved of in the form of who didn’t get valentines. As the kid who claimed to be a cat (and later an alien), that kid was me. It didn’t get me down. It instilled a sense that I was in charge of my own happiness every day of the year. Just as every day, I’d try to bear the knocks and celebrate the compliments. I try to do my best every day of the year. Some times I’m going to have a bad day. Perhaps as a practical pessimist, I don’t have use for a day that is awful unless it’s wonderful.
But let me celebrate what I do like about Valentine’s:
- Chocolate: Seasonal candy makes every holiday better. Cadbury eggs and candy corn and Valentine’s truffle boxes on sale after the holidays are awesome. As a kid I used to go to the chocolate shop the day after every major holiday and score some 75% off candy.
- Flowers: Not so much purchasing them, because they get kind of ragged and expensive this time of year. More that they are popping out of the ground. Here the crocuses are erupting by the hundreds now. The daffodil greens are up. The lenten roses are blooming. The little spring snowflakes are out. The world is at last offering up its bouquets after the winter.
- Hand-made valentines: I feel like a genius when I make valentines out of doilies and construction paper. I always think they look awesome, and they definitely look more awesome than the pre made ones. Years ago a good friend made me one and I think it made my decade.
Also, it’s finally February! Today the sun sets at 5:50 PM. Every day has an extra hour of better sunshine than this day last month. The world teases with little flowers. Soon the sun will come out and all the trees will bloom. Baseball returns! Soon we shall be wearing short sleeves again.
Every year, I trek south to Florida for the holidays. The sun and warmth are great, but I especially like the feeling of going to a different world. The land is flat and riddled with little inlets and brackish creeks. Here in southwest Florida, there is a feeling that man does not control the wilderness. Things grow at an insane rate and they fight for space. The landscape takes on that wild, violent look. I like the greenery and the beaches and the boats and the sunsets all. And I like to drag my camera along for documentation.
This post continues Wednesday’s post about fractals and the Mandelbrot set. Fractals are a branch of mathematics that we can observe in our daily life. Something is said to be fractal when a small piece of an object resembles a larger part of itself. The featured image is of romanesco broccoli; as you can see, each small cone on the broccoli resembles the overall structure of the vegetable. For this reason, the mathematical terms “fractal” and “self-similar” are closely related.
Examples of fractals in nature abound. The heartbeat of a healthy person is fractal when plotted in time; interestingly, people with various health problems show less fractal character to their heart rate. For a great slide show with images of fractal-ness in nature, check out this Wired article. Fractals have been observed in ocean waves, mountain structures, fern, lightning, city layout, seashell, trees, and many others. Many computer graphics of natural phenomena are generated using fractal processes.
The Koch snowflake (above), is a fractal generated from a line. As the fractal pattern is repeated, the length of the curve grows infinite. A line segment does not have infinite length, and yet the Koch Snowflake clearly does not fill space. So what is the dimension of this object? Through a method called the “box counting method“, we can determine the dimensionality of a fractal object. The box counting method is used to estimate area and coastal length from satellite pictures, as demonstrated below.
In short, we can see how the number of boxes needed to define a length or space changes as the box size changes. For a line, the number of boxes needed grows as 1n. For a space, the number of boxes grows as 2n. The method is explained in more detail here. Intuitively, we can tell the Koch Snowflake has a dimension between 1 and 2. It turns out that, using the Box Counting method, we can determine that the Koch Snowflake has a fractal dimension of log(4)/log(3), or about 1.26.
Fractal dimensions turn up in strange places. For example, chaotic attractors have fractal dimension. The Lorenz attractor, above, has a fractal dimension of 2.06. In the future I will discuss chaos and chaotic attractors. Check out my previous science posts on synchrony and art resembling science.