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Sunday, Dec. 22, 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

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

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10 Most Recent Blog Comments:

Annette

about 12 hours 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

October 5, 2024 at 12:55am

#1077785

It Was Just Waffle

Even on the TGV, it takes a while to get from Lyon to Brussels. Worst, Brussels wasn't my actual destination; I had to hop on an intercity train to Bruges. Those trains are open seating and run frequently; they're more like NYC subways than what I'd expect from intercity (IC) trains, only without the piss, buskers, and giant Saks sacks.

Well, I guess technically, they're more like NJT trains, but more people know the subway.

Anyway, I was concerned about time, because I had to be at a certain statue at 6:30 pm or I'd miss a beer tour (and of course I couldn't let that happen under any circumstances). So I ran to catch an earlier IC train, which I barely did because the TGV was late getting to Brussels. Then, once in Bruges, I had to get to the hotel even though the meeting place was kind of between the station and the hotel, because who schleps travel bags on a beer tour?

You'd think I'd have learned my lesson back in Tours, but, apparently, we ugly Americans just won't take a hint. Once again, the hotel was 1600 meters from the train station. Once again, the terrain between was mostly flat. And once again, I cursed every single goddamn cobblestone in Europe.

I got to the hotel at 6, exhausted. My left knee is still wonky, and so is my right ankle. Of course it can't be one leg; it's gotta be both so I can limp with every step instead of just half of them.

Now, the hotel is older than European colonization of America (unless you count the Norse incursion, which I don't because they didn't make a lasting colony), so it has a few... interesting features. One of them is an abundance of stairs. Another is that, in order to get to my room, I had to take an elevator up one floor (or carry bags up a spiral staircase, which, well, no) then walk down a hallway, up a ramp, bounce up two steps, take a few twists and turns, and then get on a separate elevator to take me up half a floor.

At least the hotel has been retrofitted with electricity.

I barely had time to throw the bags in my room before I had to turn around and make my way to the statue. One of the streets on the way was called Steenstraat. Now, I don't know very much Dutch, I'm afraid, but "steen" and "straat" are two words that I am familiar with: Stone Street.

Even without bags, cobblestones are a pain in the ass.

When I got there, the guide was waiting impatiently, tapping his foot. Apparently, he'd messaged me to meet at 6 instead of 6:30. I'd never gotten any such message. Fortunately, his English was excellent, and I showed him that no, I'd received nothing. Unfortunately, the reason he'd wanted to meet earlier was that the best beer places closed at 7, and now we wouldn't have enough time.

All that running and stumbling on cobblestones... all of that... for nothing.

Well, not completely nothing. We agreed to try again for Sunday at 2:30. And the guide pointed me at a nearby restaurant which he said was good. Now, I'm pretty sure it's the law in Belgium for every restaurant to be good, but in this case, he was definitely right. I managed to hit the entire Belgian flag

in one dinner: Beer, chocolate, and waffles. And meatballs for the main course, but meatballs aren't on the flag. All, incidentally, delivered to the table by a Japanese nekorobot . No, seriously. This thing had cat ears and a screen with an animated cat face. I felt like I was in a Black Mirror episode. Or at least Doctor Who. I should write a book: Cobblestones and Advanced Robotics: A Study In Contrasts.

Oddly enough, even though the beer I had was very local to Bruges, I'd had it before; somehow, a keg had made its way to my hometown in 2021, and, as I keep meticulous beer-drinking records (okay, it's an app), I was able to determine that I'd sampled it back then. Of course, I didn't mind drinking it again, and there are plenty of other beers here that never make it out of the EU, so it's not like I wasted the trip.

I could have done without all the quaint fucking cobblestones, though.

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