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Wednesday, Nov. 6, 2024

2:26pm EST

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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:

Turkey DrumStik

about 4 hours ago
In response to "Lo!"

Not gonna lie I need the holiday season chatter.

Aiva Raine

about 23 hours ago
In response to "It's Hard Not To Scare"

Shaking head. Aside from the inevitable Simpson's spider goat song playing in my head which I will now share with you below, whenever I come across a story that has all these scientists doing ridiculous experiments for no logical reason, I must go- ah- scientists- CANCER? You do remember that problem right? Can we maybe cure that before we make cockroaches magnetic and elephants see pink elephants?

spider pig clip- and if you all now are singing the spider goat song- you're welcome! grin
https://www.youtube.com/watch?v=BARjPuUN36Y

1 Like

Aiva Raine

about 24 hours ago
In response to "Anomalies"

One of your more humorous entries- I especially enjoyed- "Lofoten Vortex can be the name of my Bjork cover band."

Thanks for the laughs. Much appreciated.

2 Like

JayNaNoOhNo

a day ago
In response to "Anomalies"

*Toronto, Canada submits a sternly-worded petition and disputes the center of the universe claim.*

2 Like

tj-turkey-jobble-jobble-hard-J

a day ago
In response to "It's Hard Not To Scare"

Smarter mice? Just what we need!

1 Like

Wordsmitty ✍️

Nov 4, 2024 at 12:22pm
In response to "It's Hard Not To Scare"

"Friendly neighborhood spider-goat." Isn't Marvel working on that for release in '26. - "Yes, it's cute, MJ, but you shouldn't ..."

2 Like

tj-turkey-jobble-jobble-hard-J

Nov 3, 2024 at 3:52pm
In response to "Revisied: "Inevitable""

I can think of far more absurd ways to die, but most of them involve alcohol and maybe prostitutes... This statement reminded me of the passing of a friends grandfather; he died of a heart attack while intoxicated and with a prostitute, Viagra also aided in his heart failure.

2 Like

Turkey DrumStik

Nov 3, 2024 at 9:46am
In response to "She Said Spatchcock"

You can spatchcock, or butterfly, any bird.

That bit might only be funny if you're familiar with British slang.

It's really a pity that the British national team's mascot is a lion and not a rooster. Ironically, that's the French national team's mascot, which did make for a pretty good joke during the Olympics.

2 Like

Turkey DrumStik

Nov 3, 2024 at 9:31am
In response to "Cave In"

tj-turkey-jobble-jobble-hard-J

-Yeah, those instigators from Illinois and Texas would really degrade the standards of Hell.

2 Like

Turkey DrumStik

Nov 3, 2024 at 9:30am
In response to "Revisied: "Inevitable""

Though I clicked on it to check, I no longer follow that site and want nothing to do with them, which is why we haven't had any LitHub links in over a year.

Well, now my curiosity is piqued. What happened on this front?

2 Like

May 19, 2022 at 12:01am

#1032584

One Great Thing

"Invalid Item"

prompt today.

The biggest plus for living in your town/area

It's not Cleveland.

Seriously, though, I've already covered this: the proliferation of breweries both in and around town. I've mentioned several of the more urban ones, but there are just as many outside town.

But it's not just beer. No, lest anyone start to wonder if I can only think about One Thing, nothing could be further from the truth.

For example, we also have, right here in town, one of the few sake breweries in the US. While it's not the best sake, it's ours.

There are also several cideries in the area, making delicious beverage from apples and pears.

In addition, there's the wineries.

Those aren't technically in town, either, but the surrounding area is home to a large number of vineyards. As I mentioned before, it was Jefferson's idea to plant some French vines in the area, as he figured the climate was somewhat similar to parts of France. The attempt wasn't very successful.

But science advanced over 200 years, and in the 1970s, on a nearby farm dominated by the ruins of a house also designed by Jefferson, an oenologist figured out the trick to producing relatively large quantities of delicious spoiled grape juice. That vineyard is still around. I got married there once. I don't know why, but they shared their secret with other vineyards. If you've ever wondered about the explosion of wineries over the past 40 years when you're driving through unlikely places (like Indiana or New Jersey), well, you have Barboursville to thank for that.

One time, I was in California, a place much better known for its wines. Whilst sampling some good ones, I was talking to the owner (it was a small place) and told him I was from Virginia. He scoffed at the idea of Virginia wine. I of course took it poorly. The next time I was there, I brought with me a bottle of Viogner, one of the grapes that do really well around here, to give to him.

Look, I'm not saying we're as good as France or California, or even a good Argentinian Merlot or an Australian Shiraz, but our vineyards don't suck and, you know... shop local.

We're also home to Trump Vineyards, about which the less said the better. Naturally, it's the one wine I won't drink.

I can't end this without also discussing distilleries.

Our neighbors in Kentucky and Tennessee get all the publicity when it comes to distilled spirits (primarily bourbon and rye). And for the most part, it's well-deserved. But recently, we've become home to several small distilleries, including Vitae in town, and Silverback out in the country. Decent product from both of them.

Now, plenty of locations have a good selection of fine fermented and distilled beverages, but the particular combination here makes the town a great place to live.

So you see, I don't just think about One Thing.

2 Like • Comment • View 1 comment

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