The images on this page are expressions of sequences. Some people are probably familiar with the Fibonacci sequence, named after Leonardo Fibonacci, an Italian Mathematician of the late 12th and early 13th centuries. The sequence is as follows:

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89...

If you couldn't tell, the rule to produce the sequence is to add the previous two terms to find the value of the current term. This means the sequence is infinite. The first two numbers are just assumed to be 1.

One cool thing about the Fibonacci sequence is that you can build a spiral out of it. This spiral, and other manifestations of Fibonacci numbers (numbers in the Fibonacci sequence), are commonly found in nature. You build the spiral by drawing diagonal lines, first up and to the right, then down and to the right, then down and to the left, then up and to the left, with the lengths of successive Fibonacci sequence terms. Then you draw a 90-degree arc from end to end of each line, on the outside, and you get the spiral shown below:

Now, I learned about the Fibonacci sequence in fifth grade. Two years earlier, in third grade, before I knew about it, I came up with my own series. Only after two years did I discover the amazing similarity to the Fibonacci sequence. Yes, I was doing math for fun in third grade, and continue to, now that I'm in the latter half of high school. Dammit I'm a nerd. My sequence, in its entirety, was as follows:

0, 1, 1, 2, 3, 5, 8, 3, 1, 4, 5, 9, 4, 3, 7, 0, 7, 7, 4, 1,
5, 6, 1, 7, 8, 5, 3, 8, 1, 9, 0, 9, 9, 8, 7, 5, 2, 7, 9, 6,
5, 1, 6, 7, 3, 0, 3, 3, 6, 9, 5, 4, 9, 3, 2, 5, 7, 2, 9, 1

Mine is a finite sequence; 60 terms. It repeats itself after the end. Most people don't figure out the rule when they see it, but you might since you saw the bit about the Fibonnaci sequence. This time around, the rule is to add the two previous terms to get the current term, but if the value is greater than ten, subtract ten. (For those of you who like math as much or even more than me, that is just a third-grader's way of saying it's the Fibonnaci sequence, mod 10...) This has the result, since there are no lower place values to influence its change in the Fibonacci sequence, of showing the order of the digit (ones) place of the terms in the Fibonacci sequence. If you came into this knowing what the Fibonacci sequence was, I bet you didn't know that the last digit in the terms repeats after 60 terms!

Because of its similarity to the Fibonacci sequence, I decided to create a spiral of my series, using the same construction rules. The two images below are a still image of the final spiral, plus an animation of its construction, arc by arc.