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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?

May 18, 2021 at 12:20am

#1010351

Screening

30DBC prompt is running late, will edit later, etc.

So yesterday, I got to perusing my local drafthouse cinema's movie offerings. As I've mentioned before, I've been back to regular visits to the movie theater. I saw Godzilla vs. Kong twice, the second time as a celebration of my friend's vaccine freedom (I'd achieved freedom two weeks earlier). In between, I saw Nobody, which was a great fun movie, in whatever genre John Wick is. Middle-aged white guy revenge fantasy, I guess. Like I said, a lot of fun. And on Thursday I'm going to go see Wrath of Man, which, well, all I need to know about it is it's a Guy Ritchie movie with Jason Statham.

Anyway, my questionable taste in film aside, like I said, I was looking at their upcoming calendar and I noticed something cool. Now, Alamo only posts a week in advance for new releases and blockbusters, but usually like two weeks out for older movies. So their weekend lineup for Memorial Day isn't complete yet.

But just about every single showing currently listed for that weekend is already sold out.

This doesn't affect me much, because I prefer to do my theater-going on weekdays. It's quieter and the people are more interested in the movies and less in just being anywhere that's not home. So I have no real desire to visit the cinema on any weekend, especially a holiday weekend in the US. (This does not mean that I never will.) But as far as I can tell, what this means is:

Movies are back, baby.

Now, look, I get it, some people prefer to watch movies at home. I'm not dissing that. I do it myself. And if this were just a standard theater with an overpriced popcorn and Coke concession, I'd avoid it too. But like I said, the theater is also a drafthouse with 32 beers on tap, numerous other drink options, and a varied food menu including full dinner (or lunch) options. And seat table service. Most importantly, any assholes who play with their stupid phones during the movies are thrown out on their ears.

Sure, I could stay at home, drink the booze I have here, fire up the internet, and whip up some tacos or something, but I like the movie-theater experience, with the big screen and the Dolby surround sound -- things that I could approximate here, but never duplicate. Yeah, it gets expensive sometimes. I'm okay with that. There are few things I'd rather spend my money on. I could say I'm just glad to do it after a year of enforced separation, but if you've been following along, you know I wasn't entirely absent from the cinema during that time. Closings and health-related restrictions interrupted my goal of seeing at least one movie a week there, though, and all I'm doing is getting back into that schedule.

Hell, I might even start doing quickie reviews of movies, here. I think I could make them entertaining, especially since I tend to see them drunk. I mean, why not? The theater's well within stumbling distance.

Edit:

PROMPT May 18th

What is the most ridiculous or one-of-a-kind thing you’ve ever bought? Tell us the story!

Yeah, I dunno... Drunk Me sometimes buys me presents, but so far they haven't been too ridiculous, and certainly not unique, being from Amazon. Even Drunk Me knows better than to go on eBay or Craigslist. And they're not as disgusting as the presents my cats bring me.

But I suppose my first car qualifies.

I mean, technically it wasn't my first vehicle, but remember: country kid here. I drove a pickup truck.

When it died, though, it was at about the worst possible time for me financially.

Now, look, I'm not a huge motorhead. But there's something I enjoyed about vehicles made before, I dunno, about 1995 or so, ones that you could mostly fix yourself with a few tools and not have to deal with computer diagnostics or warranty-voiding. And like I said, I was close to broke, and the truck was beyond fixing by anything short of replacing everything under the hood -- at which point you might as well get a new ride.

So I went to a used car auction and bought a complete POS that had a working engine and inflated tires, and that's all I knew about it. It cost me $300 plus the auction fee, or what would be the equivalent of about $600 now. It was a 1982 Corolla that had lots of issues, but passed state inspection -- barely. Best of all, being built in the early 80s, I could do a lot of the fixin' myself.

A lot of it, but not all of it. The biggest non-cosmetic problem with that car was that it was only firing on 3 out of 4 cylinders - much like my brain when it decided to buy the car. Honestly, though, this didn't affect it much, a testament to the engineering at Toyota at the time. I mean, it wouldn't go past 60 (that's 100 for y'all furriners) without screaming in terror, but I mostly needed it for city driving anyway. And the acceleration was predictably shit, but whatever; it ran, the brakes worked, and it didn't guzzle gas.

But that's not the most ridiculous thing about it.

No, the Ridiculous Award goes to me back then for what I did right after I bought it using the last of my cash and a few bucks I'd borrowed from a friend.

I puttered that thing from the auction block across the street to Crutchfield, where I had them install a $900 sound system, complete with subwoofer, on credit.

That's right. I put a $900 sound system into a $300 auction beater.

At least I had my priorities straight, right?

6 Like • Comment • View 6 comments

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