The Mandelbrot set is technically only the completely black area surrounded by the bright red. The Mandelbrot set contains all points in imaginary coordinate space (x+yi) that approach or orbit zero when recursively fed into the function f(g)=g*g+g. When one does a rendering of the set, generally, you itterate each point untill the absolute distance to the current value is outside a preset range (usually 2) or the maximum number of itterations is reached. The number of itterations required to determine that a point did not fall in the set is rendered as a color. Chruser's render varies the brightness of one hue as the maximum number of itterations is reached. Another popular methed is a circular pallette containing a spectrum of colors, as this shows better detail as one zooms in.