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Monday, May. 27, 2024

10:42am EDT

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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:

Elisa the Bunny Stik

4 minutes ago
In response to "Distrust the Process"

That being said, I do think that people going out of their way to demonize ultra-processed foods are causing just as many issues as lobbyists are. These folks' actions exacerbate eating disorders and nervous thinking around food insecurity in equal measure. I wish the conversation around this set of actions was louder.

1 Like

Elycia Lee ☮

11 minutes ago
In response to "Distrust the Process"

To me, as long food is 100% natural, then it is healthy. Pretty much like fruits, veggies and rice. I know people have thoughts about whether rice is good or not, but it is natural food so... I shall go with that.

1 Like

Kåre Enga in Montana

a day ago
In response to "Plan Solo"

I'm more introverted than extroverted, but my only apprehension involves language and cultural barriers.

I'm bi- or ambi- but... always annoying. I waver between wanting to be left alone and not wanting to be alone.

I make my adjustments as necessary.

But LANGUAGE and CULTURE: true barriers that can cause problems for some and angst for me. I love strangers but find it frustrating when I can't connect.

For Belgium: make those plans soon. Today's connectivity means booking lodging in advance. In the old days it was show-up-and-ask-if-they-have-a-room. Still possible but not recommended unless cost is not an issue.

I prefer staying in hostels but rarely join in 'events'. I have gone out with fellow travelers however.

Kåre Enga in Montana

a day ago
In response to "Banned Camp"

I remember when the movie "Brokeback Mountain" received "F"s from folks who basically commented that they would never NEVER watch such filth. Even those who liked or enjoyed it missed the main theme of poverty (financial, cultural, individual...). Personally, I preferred the short story to the movie. Both made a point that America didn't/doesn't want to face: choice and lack of choice.

That said, if someone were to ban my poetry I could probably live off of the notoriety.

Burning at the stake though seems a more likely outcome.

2 Like

🌕 HuntersMoon

a day ago
In response to "Banned Camp"

"Any book worth banning is a book worth reading." Isaac Asimov

2 Like

Aiva Raine

May 21, 2024 at 11:34pm
In response to "More Science"

Giggles. Thank you for the laugh- especially this phrase, "I always picture Doc Brown's workshop in Back to the Future. Yes, of course I know it's wrong, but I'd rather be amused than right."

1 Like

Aiva Raine

May 17, 2024 at 6:57pm
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

April 17, 2023 at 9:16am

#1048319

In-Vesting

Time for another clothing-related prompt from "Journalistic Intentions"

[18+]. Unlike earlier prompts, this time, the RNG gave me something I've actually heard of.

Waistcoat

Now, here's a refreshing change: a name for an article of clothing that actually makes linguistic sense. Sort of. Except that "waistcoat" and "vest" are synonyms. And also, some sources claim the name is a pun: the vest was made from the waste material from tailoring the jacket and pants, hence, waste-coat. As it hugs the waist (not to be confused with a cummerbund, which is worn around the waist), the pun was really inevitable.

I've long been operating under the assumption that it's a "vest" when it's the outer layer of an outfit, and "waistcoat" when it's worn as, say, part of a three-piece suit. Three-piece suit is, itself, a misleading phrase, as one almost always also wears socks, shoes, a shirt, and a tie, making it, at the very least, a seven-piece suit. Not to mention underwear (bottom and top) (optional), cufflinks, a belt or suspenders, a hat (some of us still wear them), and my favorite, the pocket square. Though I'll grant that you normally buy those accessories separately, with the trousers-waistcoat-jacket part sold as a unit.

That assumption turns out not to be the case.

Of course, it's possible to have trousers, waistcoat, and jacket be of different materials, colors, and patterns. But then it's not a three-piece suit, is it?

Look, I know more about traditionally men's fashion than women's. This should not be a surprise to anyone.

As an aside, I mentioned up there that "vest" is effectively a synonym for "waistcoat." This isn't strictly true. In the UK, a "vest" is what we Yanks unfortunately have taken to calling a "wife-beater," from the stereotype of the man wearing only a sleeveless undershirt who engages in domestic abuse. This is, of course, not the only fashion-related linguistic trap between US and UK English. "I'm wearing pants" has a whole different meaning, too.

Adding to linguistic confusion is that "to vest" is a verb that has several meanings, including "to put on clothes." Whether those clothes involve waistcoats or not.

All of which is to say that even in this relatively simple case, nothing in fashion is as straightforward as one might think.

For example. I've been wearing suits (occasionally) (yes, I own suits) since I was a kid, and it took me until like 2019 to discover that you're not supposed to close the bottom button of a waistcoat. I knew about that rule with jackets, but no one told me about vests.

As an engineer, this really annoys me beyond all reason. While I understand, intellectually, the idea of nonfunctional junk on clothing (the rivets on a pair of Levi's served a purpose once, but nowadays they're just tradition, for example), why make it look like you're supposed to button something when you're not?

The only answer I can come up with is that they do it as a visual kind of shibboleth: if you don't conform, then those in the know have yet another reason to look down upon you.

Which is why I love pocket squares. They make excellent gags.

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