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Hello  I am a new member to the forum,literally just joined & logged in. I have purchased some fractal geometry books and looked over Mandelbrot's Fractal Nature book plus some others but only superficially. First question: can anyone recommend a relatively straightforward introductory book that shows the math involved, without
going too deep?  Looks like to iterate the 2-D sets, the equation is pretty simple.  Secondly, what is a free and simple computer program that I could use in a classroom setting to show students (in this case health professionals) how to generate fractals?  I have a start-up company to teach nurses, and want to include some fractal dosing for respiratory meds (since the lungs approximate a natural fractal) but want to introduce the subject in a glitzy or jazzy manner (because people fall asleep when math is discussed) and
a simple to use program "here's how to generate the Julia set, etc" would hopefully generate some excitement.  So, first I need to review the subject myself, and secondly, need a teaching tool that is simple to illustrate the concept(s) in a classroom. Anyone have any suggestions? Thanks in advance!

there is much more to say about fractals than just how they are made
the underlying concept of chaos is what makes them so mind blowing, the images themselves are - in my point of view - just a way to transport much deeper insights

and for the mandelbrot i am working on a nice tutorial about it but it takes much longer than expected