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Sunday, May. 19, 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:

Aiva Raine

a day ago
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

June 23, 2023 at 11:03am

#1051484

The Cat's Meow

Yes, this article is basically an ad for books. But it was like catnip for me.

The big idea: Are cats really domesticated?

Guardian link, so UK spellings ahead.

Few people would mistake a wolf for a dog. But if you saw the ancestor of the domestic cat in your backyard, your first thought would likely be “What a cool-looking housecat!” rather than “What’s an African wildcat doing in Manchester?”

I'd be like "Hey, when did I get a house in Manchester? Cool! Where's the nearest pub?"

What about behaviour, then? Which of the traits we commonly associate with our furry friends are the result of domestication, and which do they share with their wild relatives?

This is why the article is interesting to me, though much about cat behavio(u)r remains a mystery—as it should.

Let’s start with the classic cat sound.

Yes, let's. What I find fascinating is not so much the meow itself, but the different interpretations of the sound across cultures. Oddly, this article spells it meow, when proper British cats go miaow. French cats say miaou—not so different (I suspect, but I'm not sure, that the plural is miaoux). Japanese cats say something like "nyan," which is the source of a popular meme from a few years ago. Most meows in other languages are at least close to onomatopoeic, though.

I had always assumed that cats talked to each other by meowing, and that they were just including us in their social circle. However, detailed behavioural observations of unowned groups of cats living in southern England have revealed that they rarely meow among themselves.

This appears to be borne out by other observations. I have a cat who almost never vocalizes. She'll purr when you expect her to, but I think I've heard her meow twice in eight years. I got her as an adult, and apparently she wasn't well-socialized with humans as a kitten. You'd never know it now, though, because she doesn't act feral at all.

Domestic cats are thought to be like other felines: solitary, aloof and asocial. But that is not always the case. When unowned cats occur in large, dense populations – as happens when people provide a lot of food – they do live in groups, composed mainly of related females.

Whoever thinks that doesn't know many cats. No, they're not always up in your face like those other animal companions are; to me, this is a feature, not a bug. But when they do want to hang with you, they won't leave you alone.

Why, then, do we consider domestic cats to be loners? Remember that the key aspect of lion and domestic cat groups is that they are made up of female relatives. But when multiple cats are brought together in the same house, they often arrive at different times, from different families. Not surprisingly, they frequently don’t get along.

My two (female) cats come from different places, and they have, at best, a wary armistice; at worst, a howling fight. Well, one of them howls. The other is silent, as usual. But they both get along well with my housemate's cats.

And as for the disturbing claim that your cat would eat you if you died at home and your body weren’t discovered: don’t believe it. Research shows that dogs are the culprit much more frequently.

I did want to address this libelous slander. Even if it were true... so what? What do you care? You're dead. And at that point, there is only one way for you to continue to fulfill your contractual obligation to your feline overlord.

5 Like • Comment • View 5 comments

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