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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:

🌕 HuntersMoon

about 21 hours ago
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

a day ago
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

Simply Me

May 3, 2024 at 11:58am
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

May 2, 2024 at 11:37am
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

April 16, 2022 at 12:01am

#1030814

Nothing to Celebrate

I was involved in designing several planned communities in my career, so this sort of thing catches my eye.

How the Disney dream died in Celebration
Disney invented Celebration as an ideal American small town. But recession, a brutal murder and a suicide have killed the magic

First of all, when I see "ideal American small town," fear ignites in the pit of my stomach. And that's before the murder part.

This is because some Amercans' idea of the "ideal" is racist, sexist, and theocratic. But I repeat myself.

Guardian link, so British spelling.

There once was a place where neighbours greeted neighbours in the quiet of summer twilight. Where children chased fireflies. And porch swings provided easy refuge from the cares of the day. The movie house showed cartoons on Saturday. The grocery store delivered. And there was one teacher who always knew you had that special something. Remember that place?

Yeah. I also remember the screams in the middle of the night, the black eyes, the furtive glances.

The first paragraph of this article is lifted verbatim from the town's original sales brochure from 1996, written by Disney's famous "Imagineering" team.

Verbatim? I doubt it. I can't imagine Disney's team would have spelled it "neighbours."

The words were matched in visual form by the new town's seal, which was stamped on everything from storm drains and mugs to golf towels. It showed a little girl with a ponytail riding a bicycle past a wicket fence and an American oak with her dog running dutifully behind her.

Why does the American oak have a dog?

The news that Celebration – population 11,000 –had suffered its first murder with the bludgeoning to death of a 58-year-old retired teacher? Followed less than two days later by the sight of a Swat team in an armoured car staking out a house, which ended with the homeowner's suicide? How do you fit these events into the Disney dream?

You'd think they'd have learned by now: one person's heaven is another's hell.

There are shops with names such as Day Dreams selling Barbie dolls, the streets are lit by olde worlde lanterns and you are followed everywhere by muzak from the 40s and 50s piped out of speakers hidden beneath palm trees. Jingle Bell Rock, Santa Claus Is Coming to Town, Oh Come All Ye Faithful – the theme is unrelentingly Christmas.

Case in point. No, it wouldn't drive me to murder or suicide, but it would drive me right out of town.

But of course that's what Disney's all about: the stitching together of reality and fantasy so finely that you can't tell where the one ends and the other begins.

Which of course is perfectly fine in their movies. Desirable, even. But at the end of the movie, only memories remain.

Why he was so drawn to live here? "I think it was because of the way Disney does things. You knew the parks and the streets would be clean, the grass cut, all the houses would look the same, it would be family-oriented and everything would work just right. A lot of people wouldn't like to live in that sort of place, but for me . . ."

Tonight, I shall have nightmares.

On 29 November Matteo Giovanditto was found bludgeoned and strangled inside his apartment where he'd lived with his chihuahua.

Ah, the motive becomes clear. No one likes to live near a chihuahua.

Walt Disney always had a dream to build a model town. It was part of his master plan to create a new magic kingdom in Florida.

I think the guy who designed The Villages

beat him to it. That place also freaks me the fuck out.

"Walt Disney was an authoritarian. Yes he was an artist, but he was also a control freak. People tend to see the Disney creativity, they often miss the centralised control that lies behind it."

This is a big part of my hatred for the concept. It's like the worst diabolical HOA you can think of, raised to an exponent of fakery.

Then they boiled all the ideas down into a pattern book that dictated every detail right down to the plants that could be grown in the yards. There were only six house styles permitted, and only a limited range of colours – white, blue, yellow, pink and buff, all in pastel shades.

All your creativity are belong to us.

The extent to which the Disney corporation went to control the warp and weft of Celebration speaks to one of the central paradoxes of modern American life. For a country that prides itself so fiercely on its untrammelled individualism and freedom, it has a strong streak of conformism.

Such an outsider perspective is often needed. Other people have said this before, better than I can, but every time you get a bunch of individualists together, they always end up converging on some style or another. Counterculture becomes conformity.

Yet Celebration has not been immune from the devastating economic collapse in America. As a symbol of its economic ailments, a couple of days after Thanks- giving, its cinema, a striking mock art deco building by the lake, shut down.

I should have noted this before, but this article is from 2010, when the worst problem we had seemed to be a recession that everyone knew wouldn't last forever. Now? I look back on that simple time with the same nostalgia that Celebration was meant to inspire.

If I cared, I'd try to find out how that planned community is doing now, after a pandemic, rampant inflation, another housing crisis, and World War III.

But I don't care. I'm staying well away from that little slice of Hades.

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