I am a programmer by trade, and am very interested in fractals.
To be very basic about the concept, one might say a 'circle of circles' is a fractal. Where each circle is made up of circles, and those circles are made of smaller circles and so on.
This idea is similar to a Sierpinski triangle, which I interpret basically a triangle of triangles.
To test my understanding, I decided to draw out this notion of a 'circle of circles'. Realize, I did this by hand with MS paint, copy and paste. I really should have just written out a simple program using some derivative of pi to get a perfect, mathematical display.
In any case, this image is just to illustrate the concept.
It's obviously not perfect, my question is: Is the notion of a 'circle of circles', 'triangle of triangles', or 'function of functions' truly the definition of a fractal? And, consequently, is the application of this notion, in this image, a fractal? (I realize it isn't because the alignment is incorrect.)
Note: The coloring was just so I could see the pattern easier, lets assume there is no color. Though if the color had been also repeating, would this still prove true?
I included another, expanding on the use of color: