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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

April 5, 2023 at 8:56am

#1047527

Portrait of a Rant

The final prompt from this round of "JAFBG"

[XGC]...

What current topic/craze are you sick of hearing about?

Well, I'm old enough to say "All of them."

But I suppose that at the top of the list sits TikTok.

"Oh, is it because the government is trying to ban it?"

No. I don't care.

"Because China uses it to spy on us?"

Nope.

"Because it's what kids these days like?"

Whatever. Kids have always liked, will always like stupid things. I did, when I was a kid.

No, the reason I wish TikTok would go away (though I don't agree with a government ban) can be summed up in one alliterative, two-word phrase:

Vertical video.

Vertical video is, in 99.9 percent of cases, an abomination against everything that is good and right.

Let me provide a bit of background.

One of the earliest computers I played on was back in the 70s. It barely even qualified as a computer, being dedicated to word processing—a typewriter with a floppy disk drive. Not one of those solid-case tiny plastic disks, either, oh no. Nor one of the larger, but still below-average, 5-1/4". No, this word processor took massive, throbbing 8" disks.

But the other "feature" of this glorified typewriter was its screen. We're used to looking at paper—typewriter paper, e.g.— in vertical orientation. So the makers of this early word processor (I think it was Wang) oriented their green CRT monitor in a vertical orientation to emulate a typewritten page. And no, it didn't have a preview function; all your codes (think early versions of {i} and {b} and {indent} here on WDC) were visible on the screen but not in the printout, so you had to print a test copy.

Anyway, the point is, this seemed weird to me even then. Paper is paper, but screens, monitors, and TVs were, by that point, standardized in a horizontal format. Mostly something like 3V:4H.

Through time, I've had several different computers, and their screen evolution went something like this: CRTs with 4:3 ratios, monitors with even more horizontal exaggeration, actual widescreen monitors. Movies released in widescreen format often had to be edited or letterboxed to fit a 4:3 monitor. Anyway, point is, I think we finally settled on an ideal ratio, whatever it is, but it's horizontal. This conforms with human vision, which has a much greater range side-to-side than it does up-to-down.

Which is one reason that the inability of some mobile phone video makers to turn the fucking phone sideways enrages me to the point of apoplexy.

One of the earliest examples I saw was some dude trying to capture the aftermath of, I don't know, a car and truck accident or something. Holding his goddamn phone vertically, he had to frantically pan side-to-side in order to catch all the carnage (not literal carnage; I don't recall there being bodies or anything). If he'd only turned the assmunching phone sideways, he could have captured the entire scene.

Since then, I have refused to watch any video in vertical format, on my phone or on the laptop. Well, with two exceptions:

1. Explosions. I don't really care about format if I'm watching shit blow up.

2. Rocket launches (with or without explosions). These are the only events that demand vertical format, because, well, everything important happens vertically.

As an aside, I don't have the same issues with still photographs or paintings. When I did photography, I'd orient the camera as appropriate: vertical for portraits (hence "portrait" mode) and horizontal for groups or landscapes (hence "landscape" mode). But videos are different.

As I blame TikTok for the appalling rise (pun intended) in vertical video, I choose to rant about TikTok in general.

So that's it. Tired of hearing about it, so writing about it. Paradox!

6 Like • Comment • View 3 comments

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