C. Alex Simpkins, Jr., Ph.D.
From time to time I'll add some images and movie files (though only small ones due to server space) which I feel are interesting, significant, or in some way cool.
I'll try to keep them grouped, with little explanations.
I find that mathematics has an aesthetic quality to it which we often overlook. One great example of the beauty that mathematics can express is fractals. Each of these is a particular type of fractal, created with various color groupings. Click to see a larger one (they make great screen backgrounds as well!). Some natural examples of fractals are snowflakes, patterns in tree branches and leaves. I love that you can zoom into a fractal infinitely, and there is always more and more detail to be found.
"Wings of Freedom"
Fractal based on electromagnetic equations
Fractal based on trigonometric equations (tangent in particular)
The random heights of this group of mountains are created by choosing a random height value, then breaking that up into groups of random height values, and so on. Pretty soon you have an interesting mountain! The water surface is created with a randomized set of combinations of the wave equation. The clouds are created by a similar method, using the equation of a sphere. Random points are created which represent the centers of overlapping spheres. Each one is partially transparent, and depending on the characteristics you give each quantity, you get various types of clouds.
One way of modelling trees is to use equations. A simple one is to begin with a randomly sized and shaped trunk, then at the end, break it up into 2 or 3 branches of 1/2 or 1/3 the size, in random directions, and then to break each of those up into 1/2 or 1/3 the size, and so on until the final end, which is leaves. No leaves suggests a tree in winter, as below is an example:
Shapes can be used, even basic shapes to create powerful imagery and for powerful applications. Basic geometric shapes essentially define spaces. These can be representative of a solid object, a set of values, scores, a region of interest mathematically, etc. Even a basic group of a cube with a sphere subtracted creates a compelling image.