Let any computer programming teaching environment, or toy computer, have enough rope to calculate and plot the Mandelbrot set. Turtle graphics (LOGO) are nice, but fractals are something that are impossible to draw (calculate) by hand, and they introduce the real power of computers. And they are spectacularly visually appealing.
That "enough rope" is simply to set a pixel a certain color, a primitive often overlooked.
Inspired by my childhood experience (Turbo Pascal for DOS).