Tag Archives: nature

Valentine’s Thoughts

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. 

Cheer to your Monday and Valentine’s Week!SONY DSC   SONY DSC SONY DSC SONY DSC

Winter in Florida

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.

Happy Friday!

SONY DSC SONY DSC SONY DSCSONY DSC

Fun Science: Fractals in Nature and Fractal Measurement

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.

Koch Snowflake (Wikipedia)

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.

Using the box counting method to estimate the area of Great Britain (Wikipedia).

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.

Lorenz attractor from Wikipedia

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.