It is possible, however, to highlight trends within the iterative process by which the Mandelbrot Set is derived, and thus to see the underlying patterns clearly. Other areas can also be highlighted to show specific behaviors of the function which take place between the start of each cycle, and the eventual convergence or expansion. The butterfly figure is an example of this process, but certainly not the only application of this principle. No values with a size greater than two converge. All positive real numbers greater than 0.25 will go to infinity rather quickly, but smaller numbers will converge.
Some coordinates correspond to a value that repeats every other time, or every third time.
If one were to catalog the location of all repeating points within the set, and classify them by how they repeat, one would find that an interesting pattern exists. The smaller circular areas are points whose value is repeating with a longer cycle of repetition. Note that the majority of these points will only enter the repeating phase after many iterations have ensued. More iterations are always required, in particular, as one approaches the edge of the set. All of the points which display this repeating behavior are also points in the Mandelbrot Set itself, or points for which the function converges.