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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:

Kåre Enga in Udon Thani

a day ago
In response to "Going to the Dogs"

I have ants in Thailand. Will I miss them in Montana? No.

Would it be nice to have a cat and a dog, here or there? Yes, but I have struggles keeping my neglected plants alive.

Not every situation is suitable for everything or everybody.

Kåre Enga in Udon Thani

a day ago
In response to "Tipped Out"

I don't tip. In my travels I rarely find tipping the norm.

I also don't haggle.

When you add the tip... the true cost of America becomes evident. But what would I know? I travel while others who have double my income can't pay rent.

Kåre Enga in Udon Thani

a day ago
In response to "Reality Cubed"

My dreams may be different from your dreams but if we share them with others then some form of the dream may live on. Regardless, if we don't eat we die. "Joy gives us wings." "Reality bites."

Aiva Raine

a day ago
In response to "Tipped Out"

Agreed. I'll tip and well, for actual waitstaff at restaurants. I'll tip appropriately for bell-staff who assists with luggage at hotels, the more luggage, the bigger the tip. I'll give a tip to the valet as well. Beyond that- I don't tip. Certainly no tip for the fast food workers, coffee baristas, grocery store clerks, etc.

It annoys me to no end that we're being asked to tip for all kinds of jobs where they are being paid an hourly wage. I've worked as a waitress when I was young and my daughter currently does. In those jobs- she absolutely depends upon proper tipping to make a decent wage. And I hate the fact that she is dependent upon tips to do so.

It leaves women especially at the mercy of arsh**() on whether she wants to accept hostile, negative, sexist, harassing, demeaning, and negative behavior from her customers in order to make a living. It condones people treating their waitstaff like shite in order to get paid. While there is much improvement from the 30 years ago when I was working as a waitress in the skimpy outfits we were forced to wear- it's still an issue at non-chain, independent owned restaurants and diners.

Women are left to the mercies of jerk customers and their only recourse is the manager who they have to hope supports their waitstaff rather than the jerk customer. Tipping should be eliminated. All employees should be paid a livable wage and waitstaff especially should not be dependent upon tolerating crappy to obscene behavior from customers in order to make a living.

But, until that happens- I always tip at least 20% and often times more. Very rarely have I tipped lower and the service in those situations was abysmal and they still got 10%.

1 Like

GeminiGem of House Lannister

Apr 23, 2024 at 6:51pm
In response to "Going to the Dogs"

I don't understand the intersection, either. I lived in a much smaller city and found that having dogs was a hassle (although it didn't stop me), what with the complainey neighbors, the extra licensing, etc. I live in a rural location now and it works great. I can't wrap my head around living in NYC with or without a dog, although I like the idea of a place that issues a canine and supplies upon moving there. Can that please be a thing?

1 Like

Lazy Writer est 4/24/2008

Apr 23, 2024 at 3:31pm
In response to "Going to the Dogs"

I love my little dog...but I live in a biggish house with a fenced backyard.

1 Like

Aennaytte: Free & Wild in GoT

Apr 23, 2024 at 3:14pm
In response to "That's Cole"

I knew and ate Kohlrabi before I ever heard of kale. Kohlrabi is so much better in every way.

That last quoted sentence is hilarious. I am glad that I wasn't bred to be a Brussels Sprout.

1 Like

Aennaytte: Free & Wild in GoT

Apr 23, 2024 at 3:11pm
In response to "Cash Stash"

The discussion of money is an interesting one. Remember the recent collapse of a few banks? I think it was about a year or so ago?
Yes, deposits were FDIC insured up to $250,000 per depositor. But some people and companies had more money in that bank than the FDIC was insuring.
I never followed up on what happened to those people. I don't run in circles of people who own that much cash.

My accounting professor took half a period to explain to us what happened and how the bank went from Silicone Valley darling to dead so fast.

He also told us that the value we give money is not backed by anything except our hope and faith that our economy will keep going.

We didn't discuss whether the value of money needed a lower income class of people.

1 Like

Aennaytte: Free & Wild in GoT

Apr 23, 2024 at 3:04pm
In response to "Revisited: "Hack This""

In my last psychology class, we discussed the evolution of the brain. It is now settled science that we evolved to have not only larger, but also vastly more powerful brains than most other animals because we learned how to cook (process) our food.
Although we are only about 1/4 to 1/3 of a normal gorilla, we eat half of the calories in a day. Not only that, we prepare the food in a way that we get to use more of the calories that we ingest.
The result is that our brain takes up more space in our noggin than a gorilla brain takes up in his noggin. Not only that, each of our brain cells is smaller, so we can fit exponentially more of those into our head.

Now, using all that goodness ...

1 Like

Aennaytte: Free & Wild in GoT

Apr 23, 2024 at 2:58pm
In response to "Hope for Hops"

Wait! Why are beer and coffee affected by climate change? That wasn't supposed to happen. All we had to do was have a boat by the side of the house for when the sea levels rise and beg our property insurance to cover fire damage. How are we supposed to remember all of that if we don't get coffee to wake us up in the morning so that we can think and beer at night to dull our sense of doom?

September 16, 2021 at 12:03am

#1017490

Hyperlocal

This one's about one of my favorite subjects. Yes, it's from Cracked.

5 Confusingly Delicious Foods That Only Exist In A Single Place In The U.S.

One of the few bright spots of living in this world today is that we can get food from practically anywhere. Not everything, sure; some things don't ship well, and there's not enough demand for others. But restaurants from other regional cuisines crop up everywhere, and I don't care what anyone says, this is an unmitigated boon for society.

But then there's stuff like this.

5. Suburban Ohio's Proudly Uncooked Pizza

...the local specialty of Ohio Valley pizza, where the cheese and toppings are added on cold, after the sauce and crust come out of the oven.

Everyone has an opinion about pizza. For me, it's that New York style pizza is pizza, and everything else (yes, including anything in Italy) is, at best, a pale simulation thereof; at worst, as with Chicago style "pizza," it's not pizza at all.

But I make an exception for Ohio.

The pizza there is different from New York style: thinner crust, and sometimes they cut it into (mostly) squares. But it's delicious. Many years ago, I used to find any excuse to go to Ohio just for Massey's Pizza (we can get NY style here in my town, but not Ohio style). Last time I went to one, though, either they'd changed the way it was made, or my tastes had altered -- whichever, it ain't what it used to be.

But this? This, I'd never heard of.

4. Hawaii's Guilty Pleasure Spam Sushi

"Decolonize your bookshelf" is one thing, but decolonizing your plate is impossible: So many foods that feel too normal to even think about happened because of colonialism. Without empires and armies, Italy wouldn't have tomatoes, Ireland wouldn't have potatoes, and the Pacific islands wouldn't have Spam, which is just as important as the other two.

When it comes to food, I don't give a shit about "cultural appropriation."

The most popular Spam dish by a mile, though, is Spam musubi, a kind of Spam sushi that consists of a fried slice of the pink stuff, a big ball of sticky rice, and some nori to wrap them together.

Unlike the pizza, this one I've seen. Note I said "seen." I cannot ever bring myself to eat Spam. No, the one Hawaiian dish I crave is Loco Moco, which is ground beef and fried eggs over rice. It's a week's worth of calories in one dish, and it's worth every pound.

But I can't be arsed to make it myself, so I'll have to wait until I can either go back to Hawaii, or the local Hawaiian place wises up and starts serving it.

3. Cincinnati's Challenging Chocolate-Cinnamon-Cheese Chili

On paper, it should be impossible to make chili weird enough to earn a spot on its list. The whole idea of chili is you do it your way, and say "screw you" to anyone without the taste buds to handle it. Veggies? Meat? Spice? Thickness? Toppings?

Oh, but they neglect to mention that there are people in Texas who will shoot you dead if you put beans in chili.

You can't go wrong ... but you can go to Cincinnati, and that's pretty close.

This doesn't just mean chili.

I don't know if I've had official Skyline chili as the article describes, but I did once try the general chili-pasta combination and... well, it's not bad.

2. A Sloppy Joe That Isn't The Joe You Know

...there's no real reason that a Sloppy Joe needs to be ground beef on a bun. If you feel crushed under the tyrannical boot of Manwich's dominion, then there's a place where you can escape: northern New Jersey, where a sloppy joe is a triple-decker deli sandwich with cold cuts, cheese, coleslaw and Russian dressing.

I've been to New Jersey way more than I've been to Ohio, and I've never seen this. Depending on the cold cuts, though, that could be damn delicious.

You might know similar versions of these sandwiches as a Reuben or a Rachel -- as if those names had any more meaning -- but these Sloppy Joes actually have a way better documented history than the cafeteria kind. According to the Town Hall Deli in South Orange, the deli sandwich is a recreation of a house specialty from Cuba -- specifically, the specialty of a spot in Havana named Sloppy Joe's.

Okay, no. There may be a superficial similarity, but a Reuben is hot. Always, always, always. Only idiots in the South try to serve it cold (by way of fairness, the North can't do grits or biscuits & gravy, so it tends to even out).

1. Dirt, Just Dirt

...you know what? I'm going to let you bask in this one all on your own.

And for once, after linking a food thing here, I find I'm not hungry at all. I mean, I started to feel some pangs in the middle, there, but after that last one, I don't think I'll be eating anything for a while.

Now I need an article on regional liquors and where I can find interesting ones. Eventually I'll be able to road trip again... I hope.

6 Like • Comment • View 12 comments

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