by Robert Waltz
Not for the faint of art.
A complex number is expressed in the standard form a + bi, where a and b are real numbers and i is defined by i^2 = -1 (that is, i is the square root of -1). For example, 3 + 2i is a complex number.
The bi term is often referred to as an imaginary number (though this may be misleading, as it is no more "imaginary" than the symbolic abstractions we know as the "real" numbers). Thus, every complex number has a real part, a, and an imaginary part, bi.
Complex numbers are often represented on a graph known as the "complex plane," where the horizontal axis represents the infinity of real numbers, and the vertical axis represents the infinity of imaginary numbers. Thus, each complex number has a unique representation on the complex plane: some closer to real; others, more imaginary. If a = b, the number is equal parts real and imaginary.
Very simple transformations applied to numbers in the complex plane can lead to fractal structures of enormous intricacy and astonishing beauty.
PROMPT January 14th
If you could have an all-expenses paid trip to see any famous sight-seeing destination (monument, building, national park, etc), where would you choose to go?
The Valles Marineris .
Cheating? Maybe. I'd argue it's a sight-seeing destination because a lot of people want to see that sight. But hey, if you're going to pay my expenses to go to Mars and back, I'd be happy to be the one standing on the rim.
If we're going to be boring and limit the destinations to Earth, there are a lot of places I still haven't seen. Hell, I've been close to the Grand Canyon many times but never actually seen it.
Some say it's overrated. Well, compared to the Valles Marineris, it probably is. There isn't a single tourist destination on the planet that someone, somewhere, hasn't claimed to be "overrated." "Mount Everest? No thanks, too crowded." "Yeah, no, the Taj Mahal is a filthy place that's falling apart." "The Eiffel Tower? Tourist crap." (Yes, that's a pun because the French word for 'tower' is 'tour.')
The places where I most want to go are less grand, anyway, and probably less singular: a brewery tour of Belgium, or a houseboat cruise down the Danube, or maybe a Vouvray expedition to the Loire valley.
But if we have to limit it to "famous" destinations on (yawn) Earth, I'd probably do what I usually do in such situations: make a list of places I haven't been (technically, I've been to the Eiffel Tower, though it was around the time Nixon resigned), and then pick one at random.
Because ultimately, I want to see everything, but I know I'll never be able to. So random it is.