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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 17, 2020 at 12:01am

#998543

Past Perfect

I've actually had a perfect day. Several of them, in fact.

PROMPT November 17th

In your entry today, plan yourself the perfect day. Who would you see? Where would you go? What would you do? How do you spoil yourself?

Each of those days was different, but they all had three things in common: friends, booze, and food.

The food part shouldn't be surprising. Most people eat every day, anyway, and I would never call a day of fasting "perfect," regardless of anything else that happened on that day. But for me it's more than mere sustenance; it's a destination and experience in itself.

I'm sure the booze part isn't surprising if you know me. But I'm not talking about overindulgence; just something to add to the pleasure of the experience.

The "friends" part surprises even me, though, because I tend to be solitary. And yet having other people around to share the experience is a good thing; I just need some time alone afterward.

Location doesn't matter much, either. I've had excellent experiences close to home and on the road.

So let's look at what a perfect day for me might look like... assuming, of course, that a certain disease is no longer a concern. I should also point out that in this scenario, the temperature never dips below about 65F. I don't care how hot it gets, though, as long as the places we go have a/c.

Morning

First -- and this is absolutely critical for a perfect day -- I'm not woken by cats, people, weird noises, or, most importantly, an alarm. I just wake up when I'm ready. Hopefully this isn't too late for breakfast.

Breakfast itself could take one of several different forms. Cooking is work, so I'm at a restaurant or diner. They'll want to give me coffee; I'll request tea instead. They'll look all kinds of confused and thrown off stride. This is good; keeps them on their toes. Hopefully they'll have something besides that puke-orange Lipton bullshit. If not, I'll order a Coke. They'll try to pass of Pepsi as Coke. This is insupportable. Water it is, then.

Sigh. Okay, that's not a "perfect" day; that's just how breakfast usually goes for me on the road. Ideally they'll have an English Breakfast tea. Fortunately for me (and for servers everywhere) I'm not nearly as picky about my food as I am about beverages. Eggs Benedict, or a bagel with lox and cream cheese, or waffles, pancakes, toast, whatever, with some variety of eggs, and bacon. But really, any sort of breakfast food is fine.

The places I want to go don't open until 11 or so, usually, so I take my time with breakfast. That's when I'll meet up with my friends and we start drinking.

Not serious drinking, but visiting wineries, breweries, and/or distilleries and sampling small amounts of their wares. Wineries can be tough because they tend to be out in the country and you need to find someone who's not drinking to give you a ride. Some breweries are, too, but a lot of times they're in town and if you can't walk to all of them, there's rideshare. Even though I'm not drinking all that much, I'm not going to risk driving.

Afternoon

Lunch -- probably at one of the breweries; lots of them have decent menu selections. Then more samples of fine adult beverages, and maybe a walk in a park or a fun section of whatever town we're in. If we see something interesting, great, we can stop and check it out. I'm pretty flexible in that regard.

After all that hard work, I'll need a short nap.

Evening

No, I'm not cooking dinner, either. And I'm not too picky about where we eat: American, Italian, French, Japanese, Indian, whatever, as long as it's not lousy chain food. And the place, of course, has an appropriate selection of booze to go with the meal, preferably including expensive single-malt scotch that I can enjoy as a dessert. Even more ideally, they'll have some sort of music as well. Just not jazz. Fuck jazz.

And then, after dinner... dancing? No hell no. A movie? Nah, can see a movie anytime. A romantic walk on the beach? No squared to the power of nope. There's very little I hate more than having sand in my shoes, but one of those things is walking barefoot on the beach. And the only thing I hate worse than walking on the beach in the daytime is walking on the beach at night; I don't care what the scenery is like. So, what then? Well, more drinking of course, again somewhere that has decent music ("decent" still being defined as "anything other than jazz").

Night

Uninterrupted sleep.

Such a day could happen again, I think, though it may be a while. In the meantime, I'll just have to make do with hanging around with my cats, reading or watching movies, and writing.

There's still beer involved, anyway.

8 Like • Comment • View 8 comments

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