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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 27, 2020 at 12:07am

#999190

I Want It Now

The short answer to today's prompt is: Nothing.

PROMPT November 27th

What do you want for Christmas? (Or for your next birthday if you don’t celebrate Christmas)

The long answer (face it, you knew there was going to be a long answer so I could say I wrote an actual blog entry) is that I have enough stuff, including everything I need and most of what I want, and while I appreciate tokens of friendship from people, there's nothing that I can say that I want that most people could afford.

"Stuff," of course, is only part of the big picture, but that's the form most holiday and birthday gifts take, so that's how I approach this.

Last year, the local movie theater / drafthouse was open on Christmas Day, so I decided to start a new Christmas tradition for myself: walk over to the theater, drink all the beer, stagger home. Didn't even see a movie, just drank beer. Then, of course, this happened, and while the theater has reopened, and the beer flows once more, the bar itself is unavailable. I don't know if it'll be open on Christmas Day this year or not.

So much for tradition.

What I want, of course, is what almost everybody wants: this to end. I'm way down on the list of people eligible to get a vaccine when it becomes available, but you can bet your last dollar I'll be getting the jab the moment I can. Am I concerned about them having rushed through the development process? Sure. Am I concerned about side effects? Sure; when I got the shingles vaccine I was useless for two days afterwards. You know what concerns me more than all that? Getting actually sick and possibly passing it on.

That's what a lot of people miss in all this, I think. Sure, you have the choice whether to expose yourself to illness, injury, whatever. Hell, I drink and I smoke cigars. Neither one of those things is going to increase my life expectancy. But when I drink, I don't do things to endanger others. There are laws about not smoking in public places so that secondhand smoke doesn't affect people who haven't made that choice for themselves. We have laws about drunk driving to discourage people from endangering others with the choices they make.

All these restrictions, masks, whatever: they're not just there to protect you from getting sick. They exist so that if you do, you don't pass the illness on to someone who has not made that choice for themselves. By being a selfish prick, you're not "exercising your rights;" you're depriving others of theirs.

Yesterday, I talked about my friend M, and in case you missed it, in the comments I provided an update: M is currently recovering from a stroke. This required hospitalization. Resources that could be used on him are sucked away by pandemic cases, in part because some people have been smug shitstains who absolutely won't be told what to do, and spread the fucking virus.

And this, folks, is why we're doomed. Not because of the pandemic; that will pass. But because of the "screw you I do what I want" mindset. This year has driven home to me that we have absolutely passed the point of no return on climate change. Too many people just will not do the right thing because it's inconvenient. Yes, the world will keep turning. Humanity as a species will survive. But things are going to get pretty rough for a whole lot of people. Displacement, water crises, food shortages, that sort of thing.

So I am working on not caring. I'm done. The assholes win. I can't beat them, so I'm going to join them, and just Do What I Want.

And what I want for Christmas is to drink. I'll manage to do that, whether the drafthouse is open or not.

5 Like • Comment • View 7 comments

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