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Saturday, Dec. 21, 2024

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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

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

Show Recent Comments

10 Most Recent Blog Comments:

tj-Merry Mischief Maker

about 18 hours 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

about 23 hours ago
In response to "To Err Is Human"

Comments work.

"Like" button sends me this message:

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2 Like

Annette

about 23 hours ago
In response to "To Err Is Human"

Can I leave this comment?

Wordsmitty ✍️

a day ago
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

a day ago
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

Ichabod Crane-- Mince Pie

Dec 17, 2024 at 9:06am
In response to "Need for Speed"

One of the last jobs I had was with Delta. I did ask the maintanace guys about that tape once and they pointed out high speed will rip duct tape or any other tape right off. They used it personally for their boats sometimes because of its strength. But looking out a window at 400 miles an hour and 30 thousand feet up and see duct tape on the wing. Certainly made me nervous first time I saw it.

3 Like

September 23, 2024 at 4:10am

#1077168

Bière Snob

Yesterday morning got off to an auspicious start as the really quite obnoxiously loud building alarm went off.

Naturally, being American, I sat down to write an official letter of complaint to management, and prepared to give the hotel 1 star reviews on Yelp, Google, and Tripadvisor. How DARE they inconvenience a US citizen?

...yes, I'm kidding. Duh. I took long enough to put pants on, which may not have been the wisest course of action for myself, but you know me, always thinking of others' comfort. And then I proceeded down five flights of narrow, steep, half-spiral stairs that are probably older than my entire country.

I'd been awake, though not for long, when the alarm went off (hence the pantsless state, as I was only beginning to get ready to go to the hotel breakfast), so at least I didn't have another heart attack from waking up to that. But on my way down, I got to wondering whether my travel insurance would cover the loss of all my shit from the hotel burning down. Probably not, I reasoned, because insurance only covers whatever doesn't happen to you.

On the descent, I was joined by other people who also had the good sense not to use the elevator during a fire alarm (one of whom had stopped to pack his bag), and we all spilled out into the lobby, where a receptionist explained to us, in perfectly good English, that someone had made smoke in the breakfast kitchen and it wasn't actually a fire threat.

My fellow travelers grumbled and started marching back up the stairs (the elevator is one of those tiny European ones with the manual outer doors, obviously retrofitted at some point after electricity was invented), but I followed my original plan and slipped down to breakfast, where I specifically asked for le petit déjeuner bien cuit, or breakfast well done (in the sense of a well-done steak). Because I am, after all, an asshole, but at least I'm a funny asshole.

The travel agent's plans for me yesterday were: Eiffel Tower, Arc de Triomphe, Champs "Ulysses" [sic], and the Seine. But none of them involved tourist reservations; those were just their suggestions for famous shit to do while in Paris.

So, instead, I did what I always do in a new-to-me city: I found breweries.

You don't think of beer when you think of France, and generally for good reason. There are a few decent large-scale breweries in the east, adjacent to Belgium and Germany so that those countries' skill in brewing manages to spill over the border. But for the most part, French beer is, historically, liquid ass.

But, like the Anglophone countries I'm used to, France has developed a craft beer scene. I only had time to visit three of them, but my overall impression is: just like the aforementioned Anglophone countries, some of the beer is excellent, and some is... well... less than excellent.

I'd never know that, though, if I didn't try. I'm pretty sure I've said this before in here, but I enjoy tasting all beer, even the bad stuff, because, as the great philosopher said: "If everything was cool, and nothing sucked, how would we know what was cool?" (I can't remember if that was Beavis or Butt-Head.)

Now, when I say "tasting," I don't mean I got pints (or, you know, 500ml, close enough) of each one, but did the small-serving flight thing. So no, I wasn't utterly wasted when I was done. But I had achieved beerenity, which has been elusive to me lately. I might have actually smiled as I walked back to the hotel, across the Seine, and through the courtyard of the Louvre, where I paused to snap what is surely the most French photograph I could possibly shoot.

7 Like • Comment • View 1 comment

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