END OF AN ERA, FRACTALFORUMS.COM IS CONTINUED ON FRACTALFORUMS.ORG

it depends on how you do it i for myself have not much success either, but keeping out the mathematical stuff, and starting
that reality is obviously not made up of triangles, squares or circles is a good starting point, then i cover that fractal dimension
defines the roughnes of a surface, continuing with real life examples like mobile-phone antennas, and the general process of self-applying results,
accompanied with an example that everyone knows: audio feedback

I have the same problem with many people (not all!) I tried to talk about this.
I guess it also is  a problem of lack of interest. It dpesn't really concern people, doesn't change anything in their daily life (although it can, in my opinion).
so why should they care and start to spend a lot of time to understand something that they aren't interested in?
i find it very sad, but it seems like this is the way it is.
you could compare this to quantum physics. you don't need to understand it to live your daily life. and it can be freaking hard to grasp, but there are many people that actually are interested. but there's no point in running around, trying to teach those who don't care something they don't want to know.

It's always a pleasure when you finally find someone who shares that interest or fascination with fractals. I whish there were more. I guess it takes time and a lot more hard work to push fractals out of the "just computer-art and maybe some clouds and rivers"corner. but I'm positive that the time will come.
and then we can be all hipster like "I was there before it was cool&mainstream"
 

I often start out by saying that the image was created with math.  If they want more, I say that each pixel represents a number.  That number is plugged into a formula, and what comes out determines the color of the pixel.  If they're still awake, then I may discuss more about the specific formulas or fractal shapes or whatever, depending on their interest.

Fractals are complex ordered patterns that spontaneously arise at the border between order and chaos.
The Mandelbrot fractal is a simple special case, applied on simple mathematics.

In empty space, there is order, nothing happens.
In the center of the sun, there is chaos.
And at the border is where we are, spontaneously complex patterns applied on the element particles.
Natural selection and evolution is further applied on these complex pattern, making them even more complex.

God is not excluded, but redundant...