Short · Math
Keep squaring and adding. Does it escape?
Hold c fixed, start at 0, and slide the steps: watch one point square, add c, and stay within radius 2 or escape. A finite-step model of z² + c.
Try it yourself
Opens One Point Orbit. Change the same thing yourself.
Transcript
Keep squaring and adding. Does it escape? Pin c at one, and start at zero. Each step squares it, then adds the same c. Zero becomes one, then two. Two sits exactly on the radius-two circle. That's not outside. Now allow one more step. Two squared is four, plus one is five. That's outside: it has escaped. Past two, squaring outgrows c, so it never returns. An escape is final. Staying inside is never proof. Try it yourself at Explainer Tools dot com.