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Looks like the Mandelbrot set, with |re(z)| > N used as escape criterion. A working start.

Very good.
This is a render from a fractal program that I'm creating. I create variations that each can create their own points if need be. The first point here is used to create a circular gradient / blur. The second variation is a Mandelbrot variation that simply changes the color of existing points (in this case, to the color red). Thus, if the gradient didn't exist, neither would the Mandelbrot.
At this point, you might be wondering why the red square boundaries extend past the black gradient's edge. This is because the gradient is actually a square blur with an alpha channel determined by the radius. It happens to be faster to do this than create a true radial blur.

Thanks for taking interest.

Indeed.