Contrary to what you may be expecting, this isn't a gallery of artwork made for use as logos. It is a gallery of artwork created using my own original code in the archaic programming language Logo, which I recently rediscovered after long years away from it.
Logo, also known as Turtle Graphics, was a language created for teaching children and non-programmers how to program a computer, using an interface which provided immediate feedback a "turtle" which they could move around the screen by using simple commands such as "forward 100" or "right 90", while it drew a line behind it to show where it had been.
While Logo is capable of considerably more than this, and can in fact be used to write full-featured applications, its best feature remains its use as a teaching tool. I picked up a copy, after doing a bit of research and considering the available options, as my language of choice for introducing my daughter (now 8 going on 9) to computer programming.
But I couldn't resist playing with the language myself as I taught her, motivated partly by a desire to show her more of what it can do, and partly by sheer enjoyment. These images are the result.
You may notice some extremely simple fractal artwork among them; while we think of fractals as the result of extremely complex mathematical equations, their only real requirement is that they be recursive and capable of infinite changes of scale without loss of the nature of the image. As you can see from the simple fractal pieces included here, it doesn't take extreme complexity to meet those requirements.
That is why fractals are the mathematical language of nature from the growth of a tree to the veins of a leaf to the petals of a flower, even the ripples in a pond, nature is filled with patterns that repeat in a way that change only in scale as they progress from small to large, or vice versa.
As you can see from my Fractal Art, I delight in fractal artwork and so I could not resist this opportunity to write my own programs to generate it in its simplest of forms. Just remember you don't have to know the math to appreciate fractals any more than a tree or a rose or a raindrop needs to know the math in order to generate them. Just enjoy them for what they are, as you would the tree, or the rose; I assure you, they will be none the less beautiful for that.