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Sunday, Dec. 22, 2024

12:57pm EST

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Complex Numbers

by Waltz Invictus

Rated: 18+ · Book · Personal · #1196512

Not for the faint of art.

Complex Numbers

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.

http://www.ddewey.net/mandelbrot/

Signature for Honorable Mentions in 2018 Quill Awards

A signature for exclusive use of winners at the 2019 Quill Awards

Signature for those who have won a Quill Award at the 2020 Quill Awards

Show Recent Comments

10 Most Recent Blog Comments:

Annette

a day ago
In response to "Neutral Zone"

It made me happy that I was able to like it. I take the small victories.

1 Like

tj-Merry Mischief Maker

a day ago
In response to "To Err Is Human"

Right from the beginning I find myself asking, "How many times can anything go extinct?" On a side note, the other day while shopping I saw a neanderthal in the produce section. He was trying to fit in with modern clothes, but it was pretty obvious he was a neanderthal.

1 Like

Annette

a day ago
In response to "To Err Is Human"

Comments work.

"Like" button sends me this message:

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Annette

a day ago
In response to "To Err Is Human"

Can I leave this comment?

Wordsmitty ✍️

Dec 19, 2024 at 9:03pm
In response to "Five Seconds"

Way, way back when I was little, it was a three second rule that I remember. Sometime since it was upped to five seconds because of all the chemical preservatives that are pumped into everything now.

1 Like

tj-Merry Mischief Maker

Dec 19, 2024 at 3:43pm
In response to "Five Seconds"

I also ate carrots right out of the garden growing up, I also picked and ate fruits and berries growing in the wild without washing. I do remember food dropped on the floor was either rinsed off and then eaten, or if it was something not easily rinsed, like buttered toast buttered side down, we gave it to the dog.

In our house, there's not a five second rule; unless it's something dogs can't eat, it's whichever one gets it first.

2 Like

🌖 HuntersMoon

Dec 19, 2024 at 8:53am
In response to "Five Seconds"

2 Like

Aiva Raine

Dec 17, 2024 at 7:39pm
In response to "Need for Speed"

Even with the actual explanation- it still left me going- sooooo what's the difference between the special expensive "speed tape" they use for "temporary fixes" and duct tape? LOL- sure sounds like duct tape to me and they are using it for exactly the same reasons you would use duct tape. I'm guessing that the only difference between it and duct tape is the "speed tape" is slightly stronger and handles temperature differences better. It still comes down holding the plane together with tape which doesn't exactly fill me with confidence. Especially if it's a Boeing plane.

1 Like

tj-Merry Mischief Maker

Dec 17, 2024 at 6:14pm
In response to "Need for Speed"

I suppose they call it speed tape to keep people calm. If they called it what it is, temporary repair tape, they may lose passengers.

2 Like

Waltz Invictus

Dec 17, 2024 at 9:43am
In response to "Need for Speed"

Ichabod Crane-- Mince Pie

, I've heard that speed tape is extremely expensive. I can only assume the maintenance guys at Delta got a five-finger discount. But if you're going to steal from work, might as well go big and not just lift a box of paper clips.

1 Like

August 31, 2024 at 8:37am

#1075949

Revisited: "Meet George Jetson"

In August and everything after
You get a little less than you expected somehow
—Counting Crows

I usually do these archaeological expeditions on Sundays, but, as I noted yesterday, all of next week will be (or at least should be) taken up by entries for "Blog Week Birthday Bastion 2024"

[13+].

The past, imperfect, goes all the way to April of 2007 today, for a short entry about consumer automation: "Meet George Jetson"

My wife wants a robot.

Yes, this was long enough ago that I was actually married.

No, not for that. I haven't been replaced by a machine yet. Or, well, maybe I have; her friends have been holding a lot of schtupperware parties lately.

"Schtup" is a Yiddish word for sexual intercourse. Her friends had these get-togethers where the host would demonstrate various "toys" (mostly made of plastic) and get some sort of commission on sales. It would have been impossible for me not to make a pun on Tupperware parties.

By "demonstrate," I don't mean what you're thinking. Get your mind out of the gutter, please.

But specifically, she wants a robot she saw that travels around the house, cleaning it.

A few years back, my housemate got a Roomba. It was a massive pain to organize around, since neither of us is naturally organized. There's barely enough open floor space for it to do its thing, and I can't be arsed to do all the work it would take to possess less stuff. It collects dust now, on top rather than inside.

Now, overlooking for the moment the years of therapy our cats will have to endure if we actually get this little slice of science fiction...

Also, the cats were not amused. Yes, I've seen those videos of cats sitting on the damn things while they scoot around, but my cats are different.

...glossing over the price (which, really, is probably comparable to an Oreck vacuum cleaner)...

The house is, and was, uncarpeted except for one single room. Not worth spending that kind of dough. Then I'd be the sucker instead of the vacuum cleaner.

...and even forgetting for the moment how this little gadget confirms my theory that if necessity is the mother of invention, laziness is the milkman...

Huh. I've been saying that for at least 17 years. I had no idea.

...aside from all that, there's something fundamentally wrong here:

There exists a household cleaning robot, and I still don't have my flying car.

Every time I complain that I don't have a flying car, two responses come soaring in, as if jerked by knees:

1) Flying cars do exist (generally accompanied by a link to a video);

2) People can't drive in 2D; imagine the chaos if they tried it in 3D.

For 1, I say "Okay, they exist. Fine. They're not production models and, more importantly, my complaint is not that they don't exist, but that I don't own one."

For 2, my response is that I don't give a good goddamn if anyone else has one; I'd be perfectly happy being the only owner of one.

I was promised a flying car. It was right there at the 1939 World's Fair: Flying Cars are the Future.

The far future, apparently.

Point is, how come she gets a household robot, and I'm still stuck driving a vehicle that never leaves the ground (except maybe when I'm being chased by Roscoe P. Coltrane)?

Spoiler: she didn't get a household robot. I'm not saying that the lack was a proximate cause of our divorce, but it probably didn't help.

There follows a link to a Popular Mechanics article (I presume from the URL), but the link doesn't work any more and I have no idea what point I was trying to make with it. Nor can I be arsed to search it out.

And just to forestall another assumption: it's not like I expected her to do all the cleaning. We both did that. Not that I would have done as much if I'd been single, as evidenced by the fact that these days, I hire a maid service, which is almost as much an organizational pain in the ass as the Roomba was.

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