By the magic of the Pen extension, Scratch can plot coloured pixels. “Turbo Mode” is also a help here, for speed. Oddly you can set the colour (0-100) with a single command, but not the saturation and brightness, so you have to set the pen to a phoney colour if it was black before.

Of course (?) you need a fake sprite to attach the program to, in this case it’s an invisible tennis ball.

Scaling the screen to the Mandelbrot domain – x in [-1, 2.5], y in [-1,1] – is a bit trial and error when working out how big the screen is pixels, but the result is good enough.