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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 13, 2019 at 12:30am

#966105

Favorites

PROMPT September 13th

Today, the prompt comes from Charlie ~

!

List some of your favorite books/movies and explain why you like them. After posting your entry, go comment on other bloggers' entries with suggestions based on their favorites.

This is harder than it sounds.

Life, you see, is change. Stories affect what you do and how you think; they also affect other stories, inspiring them. The new story then changes one's perception of the old story. Think of how many times you've heard something like "I like Star Wars." The inevitable response is "but the prequels sucked." But they didn't say anything about the prequels, or even the sequels - just the original movie, retroactively subtitled A New Hope. And that's not even getting into Lucas' retcons.

I ran into that myself fairly recently. For many years now, I've been saying that my favorite movie is the Director's Cut of Blade Runner. This is still true. Or at least I think it is. Is there a movie I like better? At this point, if there were, I'm so invested in "Blade Runner is the greatest movie of all time" that I would be lost if I suddenly switched. And then the sequel came out, and now it's impossible to have a dialogue with someone about Blade Runner without them bringing up the very different sequel. The sequel changed the original - without altering a single frame or line of dialogue. Or, at least, it informs our perceptions of it. Me, I prefer to pretend it never happened. Honestly, I'm not sure why I watched it in the first place. So I could have grounds for having an opinion about it, I suppose.

The reason I like that movie, incidentally, is a combination of factors: the atmospheric soundtrack, the impeccable acting, the ahead-of-their-time effects, and, most of all, the things it says about humanity. All great science fiction holds up a mirror and shows us as we are, warts and all, and Blade Runner is one of the greatest.

It's even harder for me to choose a favorite book. I read Heinlein's Stranger in a Strange Land at a very early age; it warped me, and shaped me, and for a long time I called it my "favorite." Now, I see more of its problematic nature in light of more recent social developments. Again, the book is the same as it's ever been (apart from the release of the unabridged version); it's only my perception that has changed. Don't get me wrong - considering the time it was published and what I know about the author, it's a remarkable book. But one has to read it in context, these days.

One book I read almost every year, exclusively in October, is by Roger Zelazny, who was a prolific science fiction and fantasy author of the 70s, 80s and 90s. The book is titled A Night in the Lonesome October, and the original editions (I don't know if others have been published) were punctuated by illustrations by the macabre artist Gahan Wilson. I hesitate to summarize it, because doing so can easily spoil it - I'll just say it's a horror story with a dash of humor, narrated by a very loyal dog. And in it, the author draws from various threads of supernatural literature, including Dracula, Frankenstein (the popularized version, not so much the novel), and Lovecraft.

I'm a fan of everything Zelazny wrote, but October turned out to be the last book he published before his death. Appropriate, once you know the theme. I don't know if I'd be quite so enraptured by it if he'd had the opportunity to publish more - because of the effects I've described above. Since the author died, the book remains untarnished in context.

I'm going to go ahead and list one more book. Well, a series, really. It's more contemporary than the others; the author is still working on the sequels. I speak of Brandon Sanderson's Stormlight Archives, which, look, let's face it, is way better than Game of Thrones in that most of the characters that you're rooting for don't die in painful, horrible ways. Sanderson's signature technique is to come up with fantasy magic systems that are internally consistent, as well as cultures that are alien but make sense, and these books are the pinnacle of his art... so far.

If life made sense, Stormlight would be made into a massive TV series and GoT would be relegated to the obscurity it deserves. (Yes, I read those books. Yes, Martin is an excellent writer; I just didn't like the books. No, I didn't see more than a few episodes of the series.) But life doesn't make sense, and I have to be content with the novels.

So there it is: one fantasy, one supernatural/horror, and one science fiction - just so anyone who chooses to comment as per the prompt above knows what my preferred genres are.

2 Like • Comment • View 6 comments

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