Zoom into the edge of the Mandelbrot set and the same swirls reappear at every scale — that endless self-similarity is what makes a shape a fractal. In plain words, the famous Mandelbrot calculation starts at zero, squares the running value, adds a fixed constant c, and repeats. If the value escapes past a distance of 2, the point is outside the set; if it stays trapped after many rounds, the point is inside. Counting how many rounds each starting constant survives paints the iconic colorful image.

A digital artist generating album art leans on this iteration, and middle-school teachers use it to show that simple rules can grow infinite complexity. Coastlines, snowflakes, and broccoli all echo the same idea: pieces that resemble the whole.

This calculator runs the escape test for one constant. Type the real part of c into the Variable A box and the imaginary part into the Variable B box, then read the Result box for the number of iterations before escape — a small number means the point fled quickly, a large one means it lingered near the set.

With the pre-filled defaults — Variable A 10, Variable B 5 — the Fractal Calculator returns Result 50.0000. Change any input and those results update instantly, so you can see exactly how each number you enter moves the answer.