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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:

Elisa the Bunny Stik

about 17 hours ago
In response to "Pleasure and Pain"

it illustrates why it's important to have people from different backgrounds, with different worldviews, working on scientific research.

This right here is why I get rather irritated by people poo-pooing college these days. I feel like that attitude effectively shits on minority populations that may not have strong finances but do possess persistent curiosity and want to learn about various subjects in-depth. In the 90s, these groups were exclusively told to go to trade schools even if they had the aptitude for college education. Nowadays the blanket "Everyone should consider a trade" mantra employs a more subtle (but still abundant) form of discrimination. I'm so over it.

1 Like

Kåre Enga in Udon Thani

Apr 25, 2024 at 3:16am
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

Apr 25, 2024 at 3:09am
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

Apr 25, 2024 at 2:58am
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

Apr 24, 2024 at 4:26pm
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

November 16, 2021 at 12:04am

#1021729

Thought for Food

Hey, it's one of my favorite subjects, too! What a coincidence!

PROMPT November 16^th

This one will cover one of my favorite subjects, Food.
Do you follow a certain regimen/diet when it comes to eating?
Other than something you might be allergic to, are there any foods you avoid or limit yourself to? What's your favorite meal to prepare. Share your recipe if you like. (I have a 'killer' chocolate recipe!)

Tonight, I made my beer chili again. Normally I use ground beef, but there was some ground pork in the fridge for whatever reason, so I blended the two in an unholy blasphemous union, and it worked.

The chili is something I like to do when it starts getting colder. I'll get tired of it after a while and put the recipe away until next fall. I don't accept the existence of "comfort food," but there are certainly things I like for certain times of year or moods.

Do you follow a certain regimen/diet when it comes to eating?

Yep, a seafood diet. When I see food, I eat it.

I followed what you might call a diet or eating regimen for two years. I lost over a hundred pounds. Then I reached a point of diminishing returns. Then it got to where I was eating 1200-1300 calories a day and not drinking, and I was still gaining weight. So I said fuck that, if I'm going to become a cliché and regain the weight anyway, I might as well enjoy what I'm eating. Hence the return of my cooking.

Other than something you might be allergic to, are there any foods you avoid or limit yourself to?

For a long time, I wasn't allergic to any food or medicine. I mean, nothing. I'd go to the hospital and they'd ask me again and again, and each time I said "nothing," they had a look of shock and disbelief on their faces, just like when I said I have no more than one alcoholic beverage a day (which at the time was true). I was pretty proud of my lack of allergies, too. Everyone else has an allergy, mostly so they can be unique, and I didn't, which made me actually unique. It's a superpower!

Until a couple of years ago when I ate a protein bar with an obscure spice from India called moringa, and my skin turned red in patches and my lips puffed up and my tongue blew up and everything went numb and my heart started racing and my vision faded and I could feel my blood pressure plummet as I collapsed.

I survived. Obviously. But I had discovered my Kryptonite. Fortunately, it lives on almost the exact opposite side of the planet from me. Except when they put it in goddamn energy bars.

Anyway. Apart from that, I only have one hard and fast rule: I never eat anything smarter than I am. Why? Because anything smarter than I am would find a way to take revenge. We know that corvids will remember a wrong done unto them

and exact a hundredfold vengeance upon the perpetrator. How much worse, then, for the genius eldritch horrors of the deep such as squids and octopodes? Granted, they might have a problem tracking me down on land, but as soon as I get into the water, Boom! Hentai city.

I do make an exception for pigs, though, because they're just so damn tasty.

So I guess it's not that hard and fast a rule.

What's your favorite meal to prepare. Share your recipe if you like.

The great thing about being single is I can cook whatever I want, without worrying about picky eaters not liking my mushrooms or complaining about the ghost pepper.

The crappy thing about being single is that either I cook something that keeps, like the chili, or a lot of food gets wasted, because there are no recipes for single-serving things. And even if there were, shit's not sold in single-person portions at the supermarket. Anyway, what would be the point? I'm not trying to impress anyone. So here's the recipe for my favorite meal:

1) Pull box from freezer
2) Partially unwrap and shove into microwave.
3) Nuke and eat.

Okay, it's not my favorite recipe, unless by "favorite" you mean what I do most often.

And yes, I exaggerate. I don't actually do a lot of microwave meals. I admit to a fondness for Marie Callender's pot pies, but those flat-out suck if you nuke them; I (uncharacteristically) take the time to bake them in the oven.

Fortunately, I ate before writing this so it didn't make me hungry. Might have some of that chocolate, though.

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