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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

November 18, 2020 at 12:01am

#998616

Original

For as long as I can remember, I liked superhero origin stories.

PROMPT November 18th

Write about origins. You can take this literally as in where your family originated from (your history, culture, traditions), or you can focus on your own origins as a person.

Other people with actual backgrounds in liberal arts have said this better than I ever could, but comic book superheroes are essentially updated mythology. Where the Greeks, for example, wrote of gods and heroes from the point of view of their own culture, our industrial/technological society has produced characters drawn from the fringes of our scientific approach to the world.

Not that there's anything actually scientific about them. Costumed adventurers have always occupied a place between genres, drawing primarily from fantasy and science fiction -- with, of course, several others thrown into the mix. Exposure to gamma rays won't turn you in the Hulk; it will sicken or kill you. Aliens don't leave glowy rings lying around for test pilots to find. Mutated genes are more likely to kill you than give you teleportation powers. Incredibly rich orphans find other ways to make the world a better place than dressing up as a bat to fight crime. Getting bitten by a radioactive spider (which, come on, really?) probably wouldn't do anything that getting bitten by an ordinary spider wouldn't do.

I like to say that my origin story occurred when I got bitten by a radioactive sloth.

Point is, though, these characters and stories occupy a place of speculation and wonder. The radioactive spider thing, or whatever, is incidental; the character's abilities draw a reader (or viewer) in, while their approaches to conflict keeps things interesting. We all know that the origin story, and everything about them, is fanciful. Some dismiss the entire genre for its lack of realism, and that's fair. But they're still stories, and just as with the magical aspects of fantasy, once you accept the more unrealistic parts, the rest can follow.

There's no real difference, then, between stories of the labors of Hercules (born of a god and set up to be an Earthly hero) and stories of the adventures of Superman -- except for the time period in which they're written, and the cultural milieu of their audience. Our modern stories take into account speculation about aliens, scientific discoveries, alternate universes, whatever -- things the Greeks had only the barest inkling of. Even the ancient gods are explained away in the comic books, as advanced, but natural, beings.

Much has been discussed about the differences between, say, Batman and Superman, or the difference in approach to superhero stories taken by different publishing companies, and everyone has their favorites, as well as those they dismiss out of hand. Most of my friends were more into Batman. I was always a Superman fan.

This has little to do with his powers and more to do with his classic origin story. An orphan sent to Earth from a dying planet, adopted by simple farmers who raised him as their own.

As an adopted child raised on a farm, this appealed to me.

Don't get me wrong; apart from the usual childhood fantasies about flying or x-ray vision or whatever, I knew damn well I didn't have superpowers and probably wasn't actually from another planet (unless Indiana counts as another planet). Though after making the entry from a couple of days ago, maybe "avoiding broken bones" counts as a superpower. And then there's my ability to drink different kinds of booze with no additional ill effects... hmm.

No, I'm pretty sure I'm human. 98% sure, at least. Well, maybe 95%.

But -- apart from the flying and the super-strength and tights and whatnot -- I have a significant departure from Clark Kent.

See, Clark was always interested in finding out his biological origins. In every version of the story, he ends up finding out about Krypton and his birth parents and whatnot, and soaking in alien science and lore. Not that he abandons those who raise him, but he has this need to find out where he "actually" came from.

Maybe it's because I know I'm not Kryptonian, but I have no such need. One family was enough for me, and apart from a mild curiosity regarding possible genetic predispositions to certain ailments, I couldn't possibly care less about my biological heritage.

I like to think that this gives me a less tribal worldview. Other people can be -- and in most cases, should be -- proud of their heritage, be it European or Asian or African or American or whatever. But for me, besides looking like I almost certainly have Northern European ancestry, I consider myself a product, not of one place or culture, but of the entire planet.

After all, when it comes to origins, whether you buy into creation stories or follow the science, ultimately, we're all descended from one human -- all one extended family. And I don't know, maybe if more people had that attitude, people might be less interested in bombing each other into oblivion.

But then again, knowing how some families are, probably not.

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