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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.

December 9, 2021 at 12:02am

#1022986

In Spite Of

Few things in life feel better than nuclear revenge. So today's link is about the lengths (or heights) some people will go to for it.

38 Things Done Out of Spite

I mean, sure, it's nice to be able to forgive sometimes, too. But other times, you need to drive the point home that you're not a pushover.

Most of these are spite houses / fences, but there are a few other cases of extreme -- and mostly legal and nondestructive -- payback as well. I won't go through all of them; you'll have to check out the link.

4. Stuart Semple's Black 3.0

This one's one of my favorites, mostly because I find feuds in the art world extremely amusing, and also because I want an outfit, preferably including a trenchcoat, made of the blackest black that ever blacked.

The color war began when artist Sir Anish Kapoor acquired the exclusive rights to the world’s blackest substance at the time, Vantablack—and refused to share it with the artistic community.

By all accounts, Kapoor acts like a massive douche. He's the artist (and I'm not denying he's a talented artist) responsible for The Bean

in Chicago. Since he's apparently gotten used to people calling it The Bean (or maybe he just backed off on public hatred of the name so people would leave him alone), we'll have to come up with another annoying nickname for it.

Enter British artist Stuart Semple, who, angered at Kapoor’s selfishness, created the “pinkest pink” and made it available for anyone to use … except Kapoor. Purchasers were obliged to agree to a statement that read: “By adding this product to your cart you confirm that you are not Anish Kapoor, you are in no way affiliated to Anish Kapoor, you are not purchasing this item on behalf of Anish Kapoor or an associate of Anish Kapoor. To the best of your knowledge, information and belief this paint will not make its way into the hands of Anish Kapoor.”

Like I said. Art feuds.

18. A Spiteful Christmas Display

When you're on the front lines in the War on Christmas...

19. The Hollensbury Spite House

Constructed in 1830, what’s now known as the Hollensbury Spite House is just 7 feet wide and contains 350 square feet in its two stories, or “about as much space as a large outdoor billboard,” according to the Washington Post.

I haven't seen this particular building, but 350 square feet in Alexandria? It's probably worth about 3 million dollars.

22. Castle of Spite

For when you're extremely wealthy AND hostile.

Anyway, most of these are interesting for one reason or another -- family drama, libertarians vs. City Hall, thwarted romance... all the stuff worthy of stories.

I guess that to err is human, to forgive is divine, and to create something out of spite is deeply satisfying.

4 Like • Comment • View 5 comments

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