The art teacher at my school has students make geometric drawings in which curved shapes are formed by having lots of little lines cross each other. In differential calculus you learn that all smooth curves can be formed using these so called tangent lines. As you get more and more lines the curves become smoother and in the limit as the number of lines goes to infinity you can form any smooth curve.

I decided to combine this idea with that of a fractal where if you zoom into the shape you see a similar one. Below you will see the result. It was all done using a ruler and pencils and colored markers. I then scanned it and cloned it into 4 to make the final piece. Everything is using a 1/16 inch grid and the larges piece is 8 inches meaning it has 128 lines on each side. I figure I colored in somewhere around 5,000 to 10,000 squares all together. There are 6 smaller iterations inside it and each is half the size of the one before it. The smallest is 1/4 inch by 1/4 inch. I colored them in the rainbow sequence (ROYGBIV) since there were 7 of them. You really need to click on these to see the details.

The main fractal image.



Copied Scanned and tiled