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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

about 24 hours 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?

October 29, 2019 at 12:24am

#968586

Fantastic

https://www.thrillist.com/entertainment/nation/best-fantasy-book-series-sci-fi-s...

The 21 Best Science Fiction and Fantasy Book Series Ever

"Best" is usually subjective. They're still wrong about some of these.

We’ve done the hard work for you and rounded up the 21 best science fiction fantasy series of all time, in no particular order.

I'll give 'em credit for not putting it in a countdown-style slideshow to generate more clicks. As a reward, I'm sharing this and maybe they'll get a couple more clicks.

For the sake of tidiness (and our own sanity), we’ve limited this list to series that include at least three books, and that are either completely finished or have no further books currently planned (so, no A Song of Fire and Ice)

That's good, because I got bored with that bloated tripe about halfway through the fourth book. Okay, I'm being unfair - Martin is a good writer, but when I drop a book halfway through, it's for good reason: I just quit caring what's going to happen.

Couldn't watch the series, either.

Now. Some of the series in that list, I've read; some, I haven't. Unlike some people, I don't have an opinion on the ones I haven't read.

The Vorkosigan Saga (1986-ongoing) by Lois McMaster Bujold

I like this series a lot, but I really hate Bujold because she got her first novel published on, from what I've heard, the first try. Bitch.

The Wheel of Time (1990-2013 by Robert Jordan (with Brandon Sanderson)

This series ain't all that. Remember how I said if I quit a book halfway through, it's because I just don't care? Well, I got about 1989 pages into the 2000-page first book of this series, right when things are supposed to be all climax-y, when the book's plot is being wrapped up and the stage set for the next 89 books, and threw the thing at the wall.

When Jordan died and I heard Sanderson was going to wrap things up for him, I thought about going back and trying again - I like Sanderson's writing a great deal, and I figured if he cared enough to do the work I should at least see what all the fuss was about, but... you know... squirrel!

The Lord of the Rings (1954-1955) by J.R.R. Tolkien

Come on, do we really have to include this one?

His Dark Materials (1995-2000) by Philip Pullman

Let me not mince words, here: this series is indefensible. About the only good thing about it is: bears in armor. I mean, that's epic. But everything else about the series actually sucks. Unlike some of the other books I mentioned, though, I actually finished it. That's 24 hours of my life I'm never getting back.

The Hitchhiker’s Guide to the Galaxy Series (1979-2009) by Douglas Adams

Two of my favorite things are science fiction and comedy. When someone combines the two and does it well, it can be amazing. Also, these books are so ingrained in pop culture that you're lost if you don't read them - kind of like Star Wars.

Mistborn (2006-2008) by Brandon Sanderson

I'd pick The Stormlight Archives over Mistborn when it comes to Sanderson, but apparently the list is about completed series (even though the status of the Vorkosigan saga might make the Bujold entry an exception). Still, Mistborn is a fine series by an excellent author who is amazing at crafting epic fantasy.

There are also three fantasy series that are conspicuously absent from this list:

Amber by Roger Zelazny

Zelazny, like Jordan, was taken from us too soon. Unlike Jordan, he pretty much finished the Amber novels - though I think he wanted to write another set in the series. There are ten books in all, and the first book, Nine Princes in Amber, served as my personal introduction to fantasy.

The Vlad Taltos novels by Steven Brust

I've read this series so many times it's pathetic. The first book, Jhereg, contains what I consider to be the greatest opening line in all of fantasy (at least all that I've read). Again, though, the series might not be actually concluded.

Chronicles of Alera by Jim Butcher

Butcher is better known for the Dresden Files, a modern fantasy series. But it's definitely still in progress. Alera is a five-book (if I recall correctly) high fantasy series that's just a great read.

Anyway, that's my opinion, which of course you can take as truth.

I'm kind of surprised Harry Potter didn't make the list. Like Pullman's crappy series, it's targeted at a younger readership, which is fine. The first book was kind of painful to read, but the author got better as she went along. And like Hitchhiker's, it's part of pop culture now and there's no going back from that.

1 Like • Comment • View 4 comments

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