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Tuesday, May. 21, 2024

12:47am 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:

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

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

October 27, 2020 at 12:05am

#996853

Time to Movie On

This one's been kicking around on my list since May, and I'm just now getting to it. Still mostly relevant, unfortunately.

Why Hollywood Should Scrap All COVID-19 Movies

I've linked stuff from David Wong before. This is another of his, and as usual, it's insightful.

At the time of this writing, we're about seven weeks away from what may be the most important cinematic release of my lifetime: TENET, the Christopher Nolan movie that appears to be about handsome modern wizards who use time magic to suck bullets into their guns:

Insightful, but not always right. I saw Tenet. It was... pretty. But not very good, and I could barely see the plot around all the holes. To be fair, I was pretty drunk when I saw it, so it's entirely possible I missed something, but as a long-time consumer of science fiction, I wasn't impressed.

But we should treasure it for another reason: It may be the last big movie that ignores COVID-19 altogether.

And that's truly a scary thought. I don't really buy it, though.

It takes place in a world that has never heard of COVID-19 and I want Hollywood to know that I'm fine if every upcoming movie takes place in that same world.

On that point, I absolutely agree.

1. We Don't Need Movies (Or Even Plotlines) About The Pandemic

Maybe you saw headlines about how Michael Bay is working on a COVID-19 movie (or maybe they'll coyly call the pandemic something else, to make it even more obnoxious). This is a dire example of a creator badly misunderstanding what people want out of him.

Yep. Bay is associated with massive explosions for a reason. I go to the movies to watch massive explosions of... well... explosives, not massive explosions of contagious viruses that I already know happened in real life.

But I don't even need that powerful pandemic movie from a good director, ten years from now. I don't need it from anyone, ever.

Of course, we could, you know... just not go see it.

In fact, I'm good with every future movie just completely ignoring the fact that COVID-19 ever happened. I'm fine if the romantic comedies of 2022 feature unmasked characters having a meet-cute at the chocolate fountain at Golden Corral. Nobody is going to be pissed that they're not following CDC guidelines, for the same reason nobody wants to see James Bond stop to fumble with a condom.

Yep. If we wanted reality, we wouldn't go to movies. By the way, I will throat-punch anyone who uses the term "meet-cute" in my presence. Just be aware of this.

2. We Don't Need You To Evoke The Imagery Of The Pandemic, Either

Hey, remember how after 9/11, action directors started adding scenes that looked a whole lot like Ground Zero?

That, at least, had the advantage of being visually appealing. Not so with tent hospitals or small gatherings of masked individuals. Or large gatherings of unmasked individuals, also known as Trump worship services.

Right now, a whole bunch of filmmakers are likewise thinking of ways to incorporate COVID-19 imagery into the thing they're making, in the same way that not even in Star Trek can we escape shots of buildings collapsing into gray clouds.

Again, at least collapsing buildings look epic. Well. Unless they're happening in real life without benefit of clearing the place out first for a controlled demolition.

3. Actually, You Can Scrap Your Trump Movies, Too

You know what? Now that we're here, just apply everything I said above to the entire Trump era. I don't need a goddamned movie five years from now where Jonah Hill wins a bunch of awards for playing Steve Bannon. I don't need a star-studded HBO miniseries about Jared Kushner or Michael Flynn or James Comey or Sebastian Gorka or Tom Price or Scott Pruitt or Anthony Scaramucci or Rex Tillerson or Paul Manafort or Jeff Sessions or Michael Cohen or Eddie Gallagher or any of the other names I just got off the "Trump Scandals" Wikipedia page.

Movies have been made about Presidential administrations before. I never saw any of them. Again... just don't go see it. I wouldn't. And it wouldn't matter if the movie was trying to be fair, or sucking Trump's dick, or trying to beat him down. I've lived through the last four years inhaling the daily news cycle, and I agree, I don't need some cinematic effort to "put it all in perspective."

While we're on movies, you know what else I'm not going to see? The Avatar sequels.

Oh, I'm sure they'll be pretty. And I kind of enjoyed the first one, once I decided to let go and ignore the plot, science, acting, and dialogue. It's more the utter hubris of Cameron and the studios going, "You know what? We're just going to go ahead and make the next four right now, each with an enormous budget. People loved the first one, and they loved Titanic. Cameron is gold! What could go wrong?"

No, I want to see a boycott of those movies. Not for any silly political reasons, but just to send a message to Disney (the first movie was Fox, but I think Disney picked it up when they bought the studio): We're not putting up with this shit. Release one movie. If we like it, you'll make money, and then you can make the next one.

But, as usual, people are going to make the movies they want to make, despite what internet comedy writers have to say about them. And hopefully there will continue to be movies, and theaters, because the experience of going to the theater (especially the one I go to) just can't be replicated at home.

This year was supposed to be the year of me going to see a different movie in the theater every week or two. That held up well... until March. I started again when they reopened (at a much lower capacity) in August. I've seen movies I wouldn't normally see. I've disliked ones that got great reviews, and liked ones that people panned.

But no. I'm not going to want to see Covfefe-19 references in movies now, or ever. We get enough of that shit in real life. I go to the movies to escape from that shit. And to see explosions, car chases, and people in costumes fighting crime.

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