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Monday, May. 20, 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

May 17, 2024 at 6:57pm
In response to "Knead Some Dough?"

I grew up on mostly Wonder Bread despite our family having a large dry farm (dry farm being a farm that grows wheat and barley and safflower without irrigation- it relies solely upon mother nature to rain). I was never fond of it and looked forward to the times my mom would laboriously mill and grind the grain we brought back during harvest into flour and make home-made wheat bread. There was and still is nothing better than fresh whole wheat bread with a little butter and honey.

I think we did the Wonder Bread because my mom wasn't a fan of cooking and making bread is a time-consuming process.

I quit doing the white bread decades ago. There are so many kinds of healthy, no HFCS, etc whole grain breads out there that are delicious that I have no idea why any adult would choose the crappy Wonder Bread.

1 Like

Wordsmitty ✍️

May 13, 2024 at 1:18pm
In response to "The Breakfast and the Breakfurious"

And for those who rather not read the Smithsonian article, the History Channel episode that covers Pop Tarts (if you have a cable TV account):

https://www.history.com/shows/the-food-that-built-america/season-4/episode-1

Annette

May 10, 2024 at 12:05pm
In response to "Meditation Clause"

Everytime a stranger asks me to close my eyes, I keep my eyes open to see what they are up to.
Meditation is not for me.

But I think most people would have 45 minutes every day if they took that time away from social media or TV watching.

2 Like

Wordsmitty ✍️

May 9, 2024 at 1:15pm
In response to "Super Stew?"

But . . .

What's the difference between one being in the soup or in a stew? Is one thinner or thicker? How do writers use soup and stew?

1 Like

Elisa the Bunny Stik

May 9, 2024 at 10:11am
In response to "Super Stew?"

"Served in a pot? Maybe in your country."

Honestly, in the US I'd think soup would be served in a pot due to the quantity that ends up being consumed.

1 Like

Lazy Writer est 4/24/2008

May 8, 2024 at 3:02pm
In response to "Be Positive"

Mine always tell me to eat more fruits and veggies.

Annette

May 8, 2024 at 10:52am
In response to "Be Positive"

Asking doctors for advice has its own pitfalls. Because there is no money in recommending a sensible nutrition pattern, they will say things like: Look it up online.

2 Like

🌕 HuntersMoon

May 5, 2024 at 8:50am
In response to "Revisited: "Fail""

Shame on you for making fun of the Hoggs. Being a Virginian, Bob, you should know the reverence that the name Hog inspires recalling the glory days of the Washington Redskins (now the Commanders). The Hogs

1 Like

Charity Marie - <3

May 4, 2024 at 5:42pm
In response to "Overdraft Dodgers"

I have four different accounts and each one has a purpose. Savings, personal debit card, auto draft debit card, and a b8lls account. The bills account is the only one that can overdraft as it's for manual big bills like rent, cell, electric, etc. Stuff that mist be paid. The rest are blocked from overdraft and the savings account has no debit card attached. My bank accounts have been hacked too many times so I keep it this way to protect myself. It is very rare I ever pay an overdraft. I have a money market account for money greater than $10K so it gains interest and isn't touched except emergencies. That is a secure account too.

1 Like

Kåre Enga in Montana

May 3, 2024 at 4:23pm
In response to "It's a Crime"

Thailand versus Montana versus New York versus Costa Rica.

Theft? Not in Thailand! Not a huge concern in Missoula, perhaps in NYC, definitely an issue in Costa Rica.

Violence? Not a huge concern in Thailand. More so in MT, NY and CR (where it wasn't a concern years ago), definitely a problem in Saint Louis and the US in general. El Salvador is known for violence.

Death by vehicle. Not a huge concern in either NY or MT. A rising problem in Costa Rica. Thailand is one of the worst places in the world in this respect.

You may be shot and killed in parts of the US but you're more likely to be run-over in Thailand.

1 Like

November 25, 2020 at 12:02am

#999073

The One Unforgivable Sin

I don't possess creativity.

PROMPT November 25th

Write about tinkering, brainstorming, or the process of creation. What brings out your creativity?

I know I've been over this before. Few things strike as much fear into my stony heart than the admonition to "Be creative!"

What I am is methodical and technical.

Now, I get that some people might question my self-assessment, what with my writing and all. But all I ever do is rearrange letters, words and concepts into something that's -- sometimes -- unique. What others might see in my stuff as creativity is more a result of randomness -- by which I mean, I literally pick things at random and then hammer them into some semblance of a form. Or, as with poems, the form exists and I just have to find the right words and rhythms and/or rhymes.

Having no creativity is, it seems, an unforgivable sin in our society. If I believed in such a thing as a soul, I'd say that the creative spark is the soul, and I never had one.

Take Legos, for example. Most people have played with Legos. Other people can take individual Legos and turn them into something new. Me? I have to follow the instructions or it becomes something indeterminate. You know in the first Lego movie where the entire theme was "don't freeze Lego creations into permanent form; be creative with them?" Well, that made it a horror movie for me. Everything is NOT awesome.

Or music, for another example. My attempts at making music sometimes followed the right form and structure, but there's no influx of creativity.

Fortunately, I went into a very technical, rules-oriented profession, where the soulless can, if not thrive, at least find a place. Hell, even my photography was more about the rules of composition, lighting, etc., than about any kind of artwork.

How, then, do I plan and plot a piece of writing?

Generally, I start at the end and work backwards. If I know, for example, that I need characters A and B to hook up at the end of the story, I can come up with plausible scenarios as to how they get together. If I'm working from a prompt, I find another prompt, usually through randomness, and combine the ideas. That's my theory on how writing works, by the way: not just one idea, but two or more, combined in what is hopefully a new way. If a single idea can be expressed in three ways, for example, when you get two of them together, you don't have six possibilities but nine. The more ideas, and the more ways in which they can be expressed, and the possibilities become, not infinite, but large enough as not to matter. Like shuffling a deck of cards: it's unlikely that any particular arrangement of a thoroughly shuffled deck of cards has ever been made before in the entire history of cards.

I try to find through-lines. It's an old design trick, to repeat a certain theme in different ways. A particular necklace, or the concept of "necklace," for example, can take on a different meaning in different parts of the story.

Mostly, though, I just write. When I feel stuck, I freewrite. This usually helps shake something loose, just vomiting ideas onto a screen.

The thing about technical stuff is, these are things that can be taught, learned, improved. Creativity isn't learnable. You either have it or you don't. It's kind of like how some people are born blind or deaf: they can get along just fine, and they even have the advantage that no one is going to judge them for their missing sense, the way they judge the uncreative.

I can admire creativity when I see it, though when it's not paired with technical skill I'm generally not impressed. I'm also not impressed when a bunch of people get together and try to out-create each other, like at Burning Man. Want to impress me? Have the courage to change the name to Burning Woman and deal with the inevitable backlash.

At this, I got curious about this year's Burning Man, something I've never been curious about before. Usually stuff about it is background noise for me when I'm looking for interesting stuff on the internet in the summer, but I just realized I didn't hear word one about it this year. Obviously there's good reason for that, but I didn't even notice its lack until just now. Turns out the festival was all-virtual this year.

I bet they got creative with it.

I don't care.

7 Like • Comment • View 8 comments

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