Nolithius from nolithius.com here.
In your applet, over at http://www.hayles.demon.co.uk/perlin/perlin.html, it looks like the following terminology is used:
Applet -> Flash
Persistence -> ?
Octaves -> Octaves
Horizontal Scale -> x-frequency AND y-frequency
Vertical Scale -> amplitude (not used in Flash, basically a multiplier to polarize the values).
Hope that helps!
Ebyan "Nolithius" Alvarez-Buylla