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(http://i1122.photobucket.com/albums/l540/Fractal_Ken/PandemoniumOne1024.png)

Generated by homemade software with minor post-processing in GIMP.

What was generated by homemade software? All I see in your post is that line of text, and the signature below it. No image (nor a broken-image placeholder).

How strange! The fractal appears for me in two different browsers, and I'm sure I didn't already have it cached. Hopefully, its invisibility was a temporary glitch.

It seems to have been. It's there now, and fairly nifty. Real/real system?

Thanks! I'm afraid I don't understand the term "real/real system," but I'll try to describe how this Julia set was generated.

Iteration formula . . .
Let z(-1) = z(0) = standardized pixel coordinates, often called "c"
For n = 1 to 100
   Define s, t, u, and v by: z(n - 1) = complex(s, t) and z(n - 2) = complex(u, v)
   Let z(n) = complex(s*u - t*v + 0.4, 2*s*t + 0.1)

Zoom region . . .
Real axis: -0.0225 to 0.1224
Imaginary axis: 0.89 to 0.99

No points escape. I used the imaginary axis as an orbit trap for the inside coloring.

Hrm. That's almost a normal Julia set iteration, except that you're using the last two points -- and then, almost a normal complex multiplication of those points, except the "imaginary" part of the result is calculated more like that of a square ...

Since it's not an analytic map of the complex plane, even if you're using something (UF?) that treats all iteration points as complex, it's really a system of two real variables x and y involving not only x_n-1 and y_n-1 but also x_n-2  and y_n-2. Indeed, the simplest expression as a straightforward iteration involves four real variables:

x_n = x_n-1z_n-1 - y_n-1w_n-1 + 0.4;

y_n = 2x_n-1y_n-1 + 0.1;

z_n = x_n-1;

w_n = y_n-1.

I'm not using UF, just my own software. It does indeed treat all iteration points as complex.

I like your approach using four real variables. I'd never thought of the iteration formula that way.

Thanks. :)