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Wednesday, Apr. 24, 2024

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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

about 6 hours 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

a day ago
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

a day ago
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

a day ago
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

a day ago
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

a day ago
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

a day ago
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?

Aennaytte: Free & Wild in GoT

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

I have never been to New York, but it seems that my assessment years ago that Berlin, Germany and New York have some similarities. Both cities are known for being inhabited by rude people. And both places, as I now found out, are dog obsessed. And they have high rents.
Berliners though, have a habit of letting their dogs run off leash. Maybe New York is a little better than Berlin in that regard.

1 Like

Robert Waltz

Apr 21, 2024 at 1:48pm
In response to "Revisited: "Hack This""

Wordsmitty ✍️, far be it from me to speculate on the motivations of space aliens, but why in Xenu's name would they do such a thing to the universe?

1 Like

Wordsmitty ✍️

Apr 21, 2024 at 1:39pm
In response to "Revisited: "Hack This""

I thought humans got bigger brains because extraterrestrials affected our evolution, and we eat processed chicken and eggs.

1 Like

May 23, 2022 at 12:02am

#1032742

Annoying Things

For "Invalid Item"

The most annoying thing about your town/area

Of course there are no annoying things about where I live. Everyone is happy, nothing is inconvenient, and the sun is always shining.

I can hear your "Yeah, right" from here.

As I've noted before, when it's not freezing (defined by me as 55F or below) outside, I like to sit on my deck. I paid a lot of money for that thing and by Marduk's manhood, I'm going to use it.

This is normally quite pleasant. Songbirds are tweeting (and not complaining about Elon Musk), bees are buzzing, owls are hooting (yes, yes, I did my Duolingo lessons; shut up) and crickets are cricketing. Right now, the leaves are lush and green, and blocking the view of the backyard neighbors' houses.

Yes, very pleasant, except during the day and at night.

During the day, everyone gets their yard work done. This wouldn't be so bad if everyone did it at the same time. But no; that would be too kind. The neighbor mows his lawn. Then, when that's finally done, the other neighbors mow their lawn. After that one's finished, one of the people behind me mows their lawn. And then another. And then another.

There's no respite in the non-grass-growing seasons, either. If it's not lawnmowers, it's jet-engine-powered snowblowers or leaf blowers. And sometimes chainsaws. One time, the people two doors down had their ancient elm tree cut down, one of only two in the neighborhood. That took all day so it wouldn't fall on someone's house. And it was loud. On the plus side, I now own the only remaining elm around. One of these days I'm going to have to get it removed, too, and as loudly as possible, because even elms die at some point. I'm hoping to hire an artist to turn the stump into a throne where I can sit, with a beer and a cigar, and survey what's most definitely not my domain.

And then, at night? You can hear further at night for some reason. Probably because hardly anyone mows their lawn after dark. I can hear a passing train right now, and that's nearly a mile away. Well, honestly, that doesn't bother me much; I spent my childhood near railroad tracks, and the rumble and horn are kind of soothing. So that's not really an annoyance, but it does tell me that pretty much anything within a mile is going to reach my eardrums. Like sirens and semis on the interstate. Parties to which I'm not invited. Domestic disputes. Gunshots. Okay, the gunshots are pretty rare, but this is still America.

And also the nightly muscle car race. For some reason, that's still a thing. When electric cars started becoming mainstream, I rejoiced because I thought it signaled the end of the muffler-less disturbance of the peace. But no. People started complaining that you couldn't hear them coming, so they made them purposely louder, thus negating 3/4 of the purpose of having an electric car. Instead of, you know, learning to not walk in the middle of the goddamned street.

Not to mention the sirens. There's almost always a siren somewhere. Especially after the gunshots.

But all those aural annoyances are actually minor compared to the biggest annoying thing about living in Charlottesville:

This town is infested with douchebags.

It's not just the fashion, either; it's the attitude. Entitled, demanding, uncool. This is primarily evident while driving, but I also derive vast amusement from lurking on the local Nextdoor app. Like, for instance, people complaining about neighbors doing loud yard work. Or the latest, some guy complaining about always backing out of his blind driveway into traffic. I mean... have you tried backing into the driveway? Or putting up one of those convex mirrors? Or both? Come on. Or maybe taking out your muffler so they can hear you coming.

My town has not yet instituted a plastic bag ban. I hope they don't; I use those things for trash, and without plastic grocery bags, I'll have to actually purchase small plastic trash bags, thus imposing the same environmental impact but at greater cost to myself. Bans are well-meaning, I'll grant that, but like most of the bullshit people do in response to pollution or climate change or whatever, they don't do a damn thing. Remember when everyone was trying to ban plastic straws? It's like that. Rearranging deck chairs on the Hindenburg. Anyway, the point is, if they do start to discuss one, I have this fantasy about showing up at City Hall with a prepared speech about banning douchebags instead.

Won't happen. Too lazy. But I can make jokes about it.

4 Like • Comment • View 8 comments

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