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Saturday, May. 4, 2024

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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 18 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 22 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.

August 23, 2021 at 12:02am

#1016005

It Was a Dark and Stormy Night

You probably know that the Bulwer Lytton Fiction Contest is held every year, "celebrating" the worst of the worst opening lines. Well, here's this year's.

The Bulwer Lytton Fiction Contest

So fix yourself a Dark & Stormy

(it's that kind of night) and behold the radiance of the tortured prose.

I'll skip the Grand Prize winner; you'll need to go to the link to see that. But here are a few samples.

Despite an exhaustive search, rescuers were unable to locate young Christopher Robin in the Hundred Acre Wood before hypothermia took him, and the animals he once called friends descended upon his corpse like a silly old bear upon a pot of hunny.

-Paul Kollas, Orlando, FL

I mean, come on, that one's so bad it's good.

Dark and stormy, the night screamed like a ravished virgin .... the dark, stormy night ranted madly in a barometric tantrum .... it was an ebonic nocturnal tempest .... the stygian typhoon of eventide .... prosopopeic fuliginous Nyx, enceinte as it were with lachrymal lamia farouche as Hecate, disbosomed upon her terrene demiorb an empyreal borasque.

-Jack Holiday, Burbank, CA

The pitfalls of the thesaurus.

Our story begins in the cozy cottage of Bynnoldh-Dyr, son of Asgwitch-Torgwyr, in the idyllic elven village of Myrthffolwrd, but our book actually begins some two hundred pages earlier, in which you are pummeled by irrelevant history and unpronounceable names, because my publisher is paying me by the word.

-Neil B Harrison, Springville, UT

And this is what happens when you write The Silmarillion before The Hobbit.

Actually, it's fine to do that. Just publish them in the other order.

As the two beheld each other, Lady Asthenia's bosom swelled with love like two perfectly popped pans of Jiffy Pop while Lord Mycort's heart melted like butter, making their union complete.

-Roni Markowitz, Brooklyn, NY

That one made me LOL.

I'm not even pasting the best ones here. Seriously, go look at What Not To Do as a writer (that is, unless you aspire to win this contest). I am, in fact, only going to give you one more, from the "Vile Puns" section:

One time at the hoagie shop the actress Ms. O'Hara asked what the tiny pimiento-stuffed thing in my cheddar-bread sandwich was and I had to respond: "Wee olive in a yellow sub, Maureen."

-Fr. Jerry Kopacek, Elma, IA

Hey! Don't blame me; I'm just the messenger here.

Yeah, after yesterday's slog, this collection is about right. Enjoy!

I went to see Reminiscence on Saturday, but yesterday's blog entry was already too long for me to squeeze in a review.

One-Sentence Movie Review: Reminiscence

Strip the movie of its science fiction, detective, crime, mystery and action elements, and you're left with a story about a guy who really, really should just get over a girl and move on with his life, which he won't because otherwise there's no plot; nevertheless, those genres are blended smoothly together with the romance aspect, and despite its utter lack of anything approaching comedy, it's absolutely worth watching if you're into any of those things.

Rating: 4/5

6 Like • Comment • View 5 comments

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