Category Archives: fractals

On randomness

Posted on by

The nature of a random event is both complex and chaotic, but again, predictable in a certain way. When you flip a coin, the result is both random and predictable because you will get either a head or a tail, but never know which one since all events are individual and isolated, independent, and do not foreshadow in any real way what the next result might be. Sometimes we use the word “random” to refer to unpredicted outcomes such as rain shower on a sunny day or an unannounced visit from weird Aunt Hortensia who normally lives in Portland but just happens to be in Minnesota for the weekend for no apparent reason. Nevertheless, neither the rain nor the visit are random, being more a part of predictable chaotic patterns to which we may not be privy. They seem “random” but if we had more information, we would understand how they might be “strange,” but certainly not random. Teenagers love to abuse this word to describe events that seem tangential or extraneous to them, but then again, it’s because they don’t see a bigger picture. The idea of randomness has bothered me every since I read The Bridge of San Luis Rey by Thornton Wilder (1927) which tells the story of a number of people who are killed when a bridge collapses. “On Friday noon, July the twentieth, 1714, the finest bridge in all Peru broke and precipitated five travelers into the gulf below,” but is any of it random? The people are relatively unrelated and their stories and lives are all incredibly different, but they all die together when the bridge collapses. The question that the novel proposes, I suppose, is the random nature in life’s events–is there a meaning to it all or is it all random? How was it that those five people were all on the bridge at the same time and that the bridge decided to fail at that moment. At the end of Conan Doyle’s “The Cardboard Box,” Holmes remarks, “What is the meaning of it, Watson?” […] “What object is served by this circle of misery and violence and fear? It must tend to some end, or else our universe is ruled by chance, which is unthinkable. But what end? There is the great standing perennial problem to which human reason is as far from an answer as ever.” So sometimes, life looks really, really, random, even when, perhaps, it’s not.

On randomness

Posted on by

The nature of a random event is both complex and chaotic, but again, predictable in a certain way. When you flip a coin, the result is both random and predictable because you will get either a head or a tail, but never know which one since all events are individual and isolated, independent, and do not foreshadow in any real way what the next result might be. Sometimes we use the word “random” to refer to unpredicted outcomes such as rain shower on a sunny day or an unannounced visit from weird Aunt Hortensia who normally lives in Portland but just happens to be in Minnesota for the weekend for no apparent reason. Nevertheless, neither the rain nor the visit are random, being more a part of predictable chaotic patterns to which we may not be privy. They seem “random” but if we had more information, we would understand how they might be “strange,” but certainly not random. Teenagers love to abuse this word to describe events that seem tangential or extraneous to them, but then again, it’s because they don’t see a bigger picture. The idea of randomness has bothered me every since I read The Bridge of San Luis Rey by Thornton Wilder (1927) which tells the story of a number of people who are killed when a bridge collapses. “On Friday noon, July the twentieth, 1714, the finest bridge in all Peru broke and precipitated five travelers into the gulf below,” but is any of it random? The people are relatively unrelated and their stories and lives are all incredibly different, but they all die together when the bridge collapses. The question that the novel proposes, I suppose, is the random nature in life’s events–is there a meaning to it all or is it all random? How was it that those five people were all on the bridge at the same time and that the bridge decided to fail at that moment. At the end of Conan Doyle’s “The Cardboard Box,” Holmes remarks, “What is the meaning of it, Watson?” […] “What object is served by this circle of misery and violence and fear? It must tend to some end, or else our universe is ruled by chance, which is unthinkable. But what end? There is the great standing perennial problem to which human reason is as far from an answer as ever.” So sometimes, life looks really, really, random, even when, perhaps, it’s not.

On fractals

Posted on by

Though they are complex to describe, you have seen them many times in snow flakes, branching river deltas, the branches of pine trees, ancient ferns, and the florettes of a cauliflower. Fractals, though difficult to define, seem to be repeating self-similar patterns that repeat until they are infinitesimly small, but always the same. Fractals, if you were to analyse them from a mathematical standpoint, are non-linear functions that form all sorts of beautiful loops, and swirls that go on and on into a vanishing point somewhere off of the graph paper. We see fractals that occur in nature all the time. They are so common that we would miss if they weren’t there, but we ignore them because they are ubiquitous. Fractals are imprinted in our subconscious to the point that a nautilous shell can only have one design–a spiral of ever increasing size. If the fractal weren’t there, it wouldn’t be a nautilous shell, or pine tree branch, frost on a window, branching lightening, or the Mississippi River delta. Ever look at the way medieval architects imprint a fractal design on the front of Gothic cathedrals? Fractals are pleasing to the eye and soothing for the soul. Part of the universes harmony is wrapped up in fractals, including the designs of galaxies. Now, in the Oscar winning song of the year, “Let it Go,” the word fractal is included in the lyrics, and the main character creates an ice palace out of macro-fractal snow flake. Fascinating.

On fractals

Posted on by

Though they are complex to describe, you have seen them many times in snow flakes, branching river deltas, the branches of pine trees, ancient ferns, and the florettes of a cauliflower. Fractals, though difficult to define, seem to be repeating self-similar patterns that repeat until they are infinitesimly small, but always the same. Fractals, if you were to analyse them from a mathematical standpoint, are non-linear functions that form all sorts of beautiful loops, and swirls that go on and on into a vanishing point somewhere off of the graph paper. We see fractals that occur in nature all the time. They are so common that we would miss if they weren’t there, but we ignore them because they are ubiquitous. Fractals are imprinted in our subconscious to the point that a nautilous shell can only have one design–a spiral of ever increasing size. If the fractal weren’t there, it wouldn’t be a nautilous shell, or pine tree branch, frost on a window, branching lightening, or the Mississippi River delta. Ever look at the way medieval architects imprint a fractal design on the front of Gothic cathedrals? Fractals are pleasing to the eye and soothing for the soul. Part of the universes harmony is wrapped up in fractals, including the designs of galaxies. Now, in the Oscar winning song of the year, “Let it Go,” the word fractal is included in the lyrics, and the main character creates an ice palace out of macro-fractal snow flake. Fascinating.