Creating a fractal flame contains 3 main steps from start to finish:

Iterating

Plotting points via the classic Iterated Function System. This is where most of the time is spent.

Density filtering

Blurring to smooth out noisy areas of the image. This can take anywhere from under one second, to over ten seconds.

Final accumulation

Spatial filtering and color correction to produce the final output image. This is nearly instantaneous.