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Complex Numbers

by Robert Waltz

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:

Aiva Raine

May 17, 2024 at 6:57pm
In response to "Knead Some Dough?"

I grew up on mostly Wonder Bread despite our family having a large dry farm (dry farm being a farm that grows wheat and barley and safflower without irrigation- it relies solely upon mother nature to rain). I was never fond of it and looked forward to the times my mom would laboriously mill and grind the grain we brought back during harvest into flour and make home-made wheat bread. There was and still is nothing better than fresh whole wheat bread with a little butter and honey.

I think we did the Wonder Bread because my mom wasn't a fan of cooking and making bread is a time-consuming process.

I quit doing the white bread decades ago. There are so many kinds of healthy, no HFCS, etc whole grain breads out there that are delicious that I have no idea why any adult would choose the crappy Wonder Bread.

1 Like

Wordsmitty ✍️

May 13, 2024 at 1:18pm
In response to "The Breakfast and the Breakfurious"

And for those who rather not read the Smithsonian article, the History Channel episode that covers Pop Tarts (if you have a cable TV account):

https://www.history.com/shows/the-food-that-built-america/season-4/episode-1

Annette

May 10, 2024 at 12:05pm
In response to "Meditation Clause"

Everytime a stranger asks me to close my eyes, I keep my eyes open to see what they are up to.
Meditation is not for me.

But I think most people would have 45 minutes every day if they took that time away from social media or TV watching.

2 Like

Wordsmitty ✍️

May 9, 2024 at 1:15pm
In response to "Super Stew?"

But . . .

What's the difference between one being in the soup or in a stew? Is one thinner or thicker? How do writers use soup and stew?

1 Like

Elisa the Bunny Stik

May 9, 2024 at 10:11am
In response to "Super Stew?"

"Served in a pot? Maybe in your country."

Honestly, in the US I'd think soup would be served in a pot due to the quantity that ends up being consumed.

1 Like

Lazy Writer est 4/24/2008

May 8, 2024 at 3:02pm
In response to "Be Positive"

Mine always tell me to eat more fruits and veggies.

Annette

May 8, 2024 at 10:52am
In response to "Be Positive"

Asking doctors for advice has its own pitfalls. Because there is no money in recommending a sensible nutrition pattern, they will say things like: Look it up online.

2 Like

🌕 HuntersMoon

May 5, 2024 at 8:50am
In response to "Revisited: "Fail""

Shame on you for making fun of the Hoggs. Being a Virginian, Bob, you should know the reverence that the name Hog inspires recalling the glory days of the Washington Redskins (now the Commanders). The Hogs

1 Like

Charity Marie - <3

May 4, 2024 at 5:42pm
In response to "Overdraft Dodgers"

I have four different accounts and each one has a purpose. Savings, personal debit card, auto draft debit card, and a b8lls account. The bills account is the only one that can overdraft as it's for manual big bills like rent, cell, electric, etc. Stuff that mist be paid. The rest are blocked from overdraft and the savings account has no debit card attached. My bank accounts have been hacked too many times so I keep it this way to protect myself. It is very rare I ever pay an overdraft. I have a money market account for money greater than $10K so it gains interest and isn't touched except emergencies. That is a secure account too.

1 Like

Kåre Enga in Montana

May 3, 2024 at 4:23pm
In response to "It's a Crime"

Thailand versus Montana versus New York versus Costa Rica.

Theft? Not in Thailand! Not a huge concern in Missoula, perhaps in NYC, definitely an issue in Costa Rica.

Violence? Not a huge concern in Thailand. More so in MT, NY and CR (where it wasn't a concern years ago), definitely a problem in Saint Louis and the US in general. El Salvador is known for violence.

Death by vehicle. Not a huge concern in either NY or MT. A rising problem in Costa Rica. Thailand is one of the worst places in the world in this respect.

You may be shot and killed in parts of the US but you're more likely to be run-over in Thailand.

1 Like

November 12, 2020 at 12:01am

#998176

Costumerism

Me? Invited to a party? Obviously this prompt is purely hypothetical.

PROMPT November 12th

Imagine you are invited to a party celebrating your favorite book. The dress code asks you to dress up as your favorite character. Who or what do you dress up as?

First of all, I'm not sure I have a favorite book. My tastes have changed over time, like most people -- though I still consider the director's cut of Blade Runner to be my favorite movie -- and with the internet being what it is, I don't read as much as I used to.

Second, and this is the most important part: I'm utterly incapable of "dressing up" as anything. I have absolutely no talent for fashion, and more, I completely lack the ability to look at clothes on a rack and go, "that looks like something Harry Dresden [for example] would wear." I guess it's kind of like face-blindness. So when I go to F/SF cons (or did, in the Before Time), I'm usually dressed up as Me. These days, that's: Birkenstocks, black jeans, a t-shirt with a brewery logo on it, a Hawaiian shirt, and maybe a hat.

I can appreciate others' costumes, but I can never, ever recreate them.

The problem is even worse if you consider literary characters instead of ones from movies. I possess a slight resemblance to a younger Jeff Bridges, so when the local theater had a Big Lebowski movie party, I fit right in -- even though I couldn't go to a clothing store and re-create any of his outfits from the film. But at least that's a visual medium, so I could, if I really concentrated, probably find a bathrobe or something that would work. Instead, I went as me, long hair and goatee having to suffice to present myself as something vaguely resembling The Dude.

While I don't have a favorite book that stands for all time, the closest I come at the moment is A Night in the Lonesome October by Roger Zelazny. It's set in Victorian England, and the characters in that book are variations on horror/suspense archetypes: a witch, a Russian mystic, Dr. Frankenstein, Dracula, a werewolf, etc. A vampire would be easy for most people to dress as, but not me. I'd fuck something up, and pretty much have to get a set of fake fangs to demonstrate "vampire." Anyway, one of the main characters in the book is a man named Jack, strongly suggested to be Jack the Ripper. Yes, he's one of the protagonists.

Jack's outfit, as depicted on the cover art anyway, is high-fashion Victorian -- I think. I don't know. I seriously can't pay attention to these things. I know a lot of literature devotes pages and pages to the description of what an individual character is wearing; honestly, my eyes just automatically skip over that stuff as if it were an advertisement on a website or in a newspaper.

So Jack would be my first choice, only a) no one else would recognize it, because even people who have read the book would probably just see "Victorian-era clothes," which could easily be "vampire" or any number of other archetypes, and b) I don't have the slightest clue where to find or how to craft such clothing. Also, c) I have blonde hair, blue eyes and a goatee, which kind of detracts from the "tall dark, handsome, and murderous" look.

Consequently, I wouldn't bother going to the party if I had to "dress up." Unless the theme is The Big Lebowski, of course. Or, you know, if you want a Hawaiian-shirt-wearing dude to provide comic relief.

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