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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:

Kåre Enga in Montana

about 12 hours ago
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

Simply Me

about 17 hours ago
In response to "It's a Crime"

I get it. The fear spreading jerks wants us to have an "us vs. them" attitude. The division gives them leverage. (they think)

1 Like

🌕 HuntersMoon

a day ago
In response to "Butt Of Course"

My wife tried waterskiing once... called it the 100-yard douche.

Talk about retaining water...

2 Like

Elisa the Bunny Stik

May 1, 2024 at 10:53am
In response to "Mad as Hell"

"But if you want to really see how anger is useful, you need to consider how it's used as a tool for manipulation."

This is a line that must be regarded with care. After all, there are people that get angry about the way they are being treated on a large scale and harness that anger to change their circumstances. There is some level of manipulation in this angry but still legitimate flavor of activism. We do have to consider the possibility that this angel's usefulness can have net benefits (such as environmental cleanup and protection; see the Live Canal as an example).

GeminiGem survived GoT

Apr 29, 2024 at 1:53pm
In response to "Supplementary"

Working in health care for a zillion years, I've heard it all. The whole thing about something being natural, therefore it would be good for a person is very, very, very...very prevalent. An internist I worked with had a fantastic comeback to that line of thinking. She would say, "Arsenic is natural, are you going to start taking that?"

1 Like

Lazy Writer est 4/24/2008

Apr 28, 2024 at 2:14pm
In response to "Revisited: "Exercise""

I will be 75 in July. My stepdaughter gave me a bike because I wanted to ride it again. Well, I started off shaky and stayed shaky...then I fell off it...A passing motorist stopped to help me get up...I have NOT been back on that bike and will not ever again.

🌕 HuntersMoon

Apr 28, 2024 at 10:43am
In response to "Revisited: "Exercise""

So, you're saying that now you pedal your ass differently?

Elisa the Bunny Stik

Apr 27, 2024 at 10:33am
In response to "Pleasure and Pain"

it illustrates why it's important to have people from different backgrounds, with different worldviews, working on scientific research.

This right here is why I get rather irritated by people poo-pooing college these days. I feel like that attitude effectively shits on minority populations that may not have strong finances but do possess persistent curiosity and want to learn about various subjects in-depth. In the 90s, these groups were exclusively told to go to trade schools even if they had the aptitude for college education. Nowadays the blanket "Everyone should consider a trade" mantra employs a more subtle (but still abundant) form of discrimination. I'm so over it.

1 Like

Kåre Enga in Montana

Apr 25, 2024 at 3:16am
In response to "Going to the Dogs"

I have ants in Thailand. Will I miss them in Montana? No.

Would it be nice to have a cat and a dog, here or there? Yes, but I have struggles keeping my neglected plants alive.

Not every situation is suitable for everything or everybody.

Kåre Enga in Montana

Apr 25, 2024 at 3:09am
In response to "Tipped Out"

I don't tip. In my travels I rarely find tipping the norm.

I also don't haggle.

When you add the tip... the true cost of America becomes evident. But what would I know? I travel while others who have double my income can't pay rent.

July 23, 2020 at 12:02am

#988913

Butcher

Well this is a little less controversial than yesterday's prompt, but not much so.

PROMPT July 23rd

You've been given a full budget and creative license to bring a book you read to film. What book would you pick and who would you cast as the characters? If you choose a book with an existing movie adaptation, what changes would you make?

Plenty of books I could choose, but I'm going to go with the one I most recently read. Or actually the entire series of books, which is up to 16 now (soon to be 17). Also, I'm loosely interpreting "film" here; the line between movie and TV series is getting blurrier all the time, and with 17 books you need it to be a series.

I'm talking about Jim Butcher's Dresden Files, which has been going on for 20 years now.

SyFy (or, well, I think it was still The SciFi Channel at the time) did a short-lived series adaptation in 2007, but as far as I'm concerned that doesn't count. I've never seen it, anyway. So I'm ignoring it for these purposes.

For anyone who hasn't read the books (and you should, because one of them contains the greatest scene in all of literature), Harry Dresden is a wizard who lives in Chicago and gets himself into supernatural trouble on a regular basis, consorting with vampires, werewolves, faeries, etc. I figure since the show Supernatural is ending, this could fill the void with something actually, you know... good. The books combine elements of contemporary fantasy, noir detective, and comic book tropes.

Now, here's one problem for casting: time passes in the books. That is, the Harry Dresden from Storm Front is about 20 years younger than the Harry Dresden from the latest book, Peace Talks. So you either have to grab a 30 year old actor and age him up something close to naturally, or cast anyone and use de-aging tech, which has come a very long way in recent years. You did say "full budget," though, so I'm not letting age get in the way. Also, 50-year-old actors are going to be better known to me than 30-year-old actors. To complicate matters, some of the characters are supernatural and don't age much if at all. (The Witcher has this problem too.)

The most important character is, of course, Dresden himself. The books are written in his first-person point of view. I considered Henry Cavill, but he's too well-known as Superman and Geralt of Rivia, and I don't want to take him away from more Witcher series.

So for Harry Dresden, I'm going to go with Thomas Jane, who played a similar private-detective role (without the magic but with science fiction elements) on The Expanse.

Bob the Skull, Harry's sounding board at least at first, well, I'm going to go with Patton Oswalt because Oswalt is awesome. Probably limited to voice acting.

Karrin Murphy, a cop that eventually gets dragged into all the paranormal shit and becomes Harry's partner (in several senses of the word) -- well, I had to ask a friend about this, but Kristen Bell from The Good Place would be perfect.

Ebenezer McCoy is Dresden's mentor and (spoiler, sorry) grandfather, an old Scottish man. No, I'm not casting Sean Connery. I like Peter Capaldi, the 12th Doctor Who, for the role.

There are, like, a million other characters, as you'd expect for such a long series of novels. I mean, Mark Sheppard has to be in there somewhere because he's Mark Sheppard, but I don't know who he'd play.

In the end, though, I just want this to happen. I need this to happen. No matter who gets cast, as long as the series is as awesome as the books. Because polka will never die!

9 Like • Comment • View 6 comments

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