Simple toy model to develop intuition for the relationship between a complex number and its square. The grid shows the complex plane in the range -2.4 < Re(z) < 2.4 and -1.8 < Im(z) < 1.8. Move the yellow ball to any particular value of z = x+iy, and the green ball will move to the value of z^2. Press "r" to toggle the lines connecting the balls to the origin.