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Sunday, Nov. 17, 2024

3:38pm 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

a day ago
In response to "Barley There"

And approximately 15 seconds later, someone's going to screech about genetically engineered crops.

That would be me...screeching for more genetically engineered crops.

Write_Mikey_Write!

Nov 14, 2024 at 2:04pm
In response to "Global Domination"

A little girl wearing a Hello Kitty shirt in Middle-of-Nowhere, Siberia will certainly make you wonder how it got there. My grandson has a souvenir t-shirt with a Terex 33-19 "Titan" on it. When it was built in 1973, the Titan was the largest, highest payload capacity truck ever built, a title it held for 25 years. The thing is, the truck on that t-shirt is on display in Sparwood, BC, Canada - over 1000 miles from here, and his mom got the shirt at a local thrift store. Makes me wonder.

Oh, yeah - I thought 'Schrödinger's Hello Kitty' was funny, too.

1 Like

Adherennium Plotting something

Nov 14, 2024 at 12:10pm
In response to "Global Domination"

For whatever warped reason, 'Schrödinger's Hello Kitty' has tickled my funny bone.

3 Like

Brandiwyn🎶

Nov 12, 2024 at 10:50am
In response to "Blond Man's Bluff"

That's interesting about the two spellings of blonde. I always thought blonde referred to the person and blond referred to the hair. But I never bothered to look it up, So you've catered to my lazy today.

3 Like

Kåre เลียม Enga

Nov 9, 2024 at 1:02pm
In response to "It Was a Dark and Starry Night"

Ah... but why did he see those swirls when many of us don't? A totally different discussion... out of thin air... which is a frozen fog today when I gaze out the window.

Humans have great skills of observation; some of us extraordinary skills. Is The Scream depictive or evocative? 😱

Turkey DrumStik

Nov 9, 2024 at 11:04am
In response to "It Was a Dark and Starry Night"

Frankly, I'm more surprised to see reasonably good reporting from CNN. I'd given up on their ability to rein in their tendency toward loaded speech.

2 Like

JayNaNoOhNo

Nov 8, 2024 at 12:00pm
In response to "Bungalow Bash"

For the love of God, what did I just read? That is by far the worst use case of a bungalow I've ever seen, and a fundamental misunderstanding of the value of front porches—and the size of bungalows.

Was this his point? Nope, I know what his point was. For a guy so worried about presentation, he certainly undercut his own arguement.

1 Like

Turkey DrumStik

Nov 8, 2024 at 9:47am
In response to "Bungalow Bash"

"People don't change their minds on the internet. They usually do that in books, battlefields, or not at all.

Yeah, that's a little bleak."

Bleak and also inaccurate.

1 Like

Kåre เลียม Enga

Nov 7, 2024 at 10:19pm
In response to "Past and Future Intents"

I must live in the present. In the past I daydreamed a lot... probably to escape the bruises of reality; however, I need to be more aware crossing streets or even how I get out of bed (no rapid movements without thinking of consequences).

I can envision a future more peaceful than the present because this time-and-place isn't the only "present" that's ever existed, and I do try to see the larger view (emphasis on 'try').

1 Like

Lilli 🧿 ☕

Nov 7, 2024 at 10:58am
In response to "Past and Future Intents"

If the aforementioned exercises don't help; there's still liquor.

3 Like

March 25, 2024 at 8:50am

#1066890

Served with Flare

Today, I'm sharing a link that shows, once again, that it's fun to set things on fire.

Flambé Your Breakfast, Lunch, and Dinner
This retro cooking trend is back.

Back? As fire as I'm concerned, it never went away.

Here at Gastro Obscura, we really like playing with fire.

When I was a kid, the thing I got in trouble for the most (and this is saying something) was playing with fire.

There was the time that editor Sam O’Brien made feuerzangenbowle, a flaming German rum punch with roots in the rowdy student culture of the 1700s. Then there was the night I risked my fingers and eyebrows with the Victorian party game known as Snapdragon, where players compete to pull raisins and almonds out of a puddle of burning brandy.

"Snapdragon." Get it? Huh?

There's one problem with flaming food and drink: I have facial hair I'd like to keep. Okay, two problems: it's harder to exercise reasonable precautions when you're drinking flaming booze while already drunk.

Both of those were Christmastime traditions, though. I’d argue that adding flaming alcohol to food and drink should be a year-round thing.

Absolutely! And April Fools' Day is coming up fast...

Setting food on fire with warm booze was considered the height of luxury for a good chunk of the 20th century.

Now, I don't know about that. The iconic "height of luxury" was usually champagne and caviar. Champagne can be delicious, but caviar? Meh.

Besides looking pretty, what does flambéing do to a dish? There’s the taste of the liquor—which could be rum, bourbon, Calvados, or brandy—with some of the potency burned away, resulting in a smoother taste.

I've heard some people assert that it burns away all the alcohol. It does not. I suspect that at least part of the reason it fell out of favor was anti-alcohol attitudes.

I’ve flambéed a few things in my time, so I decided to set myself a challenge: to flambé my breakfast, lunch, and dinner over the course of one day.

My biggest problem with the technique is that it burns away at least some of the alcohol. This is alcohol abuse. The only time I tolerate it is if it makes something else better, which, generally, flambé does.

Doing it for every meal, though? That's a stunt. I guess it worked, because I read the article and shared it. Though we have no way of knowing if the author is completely honest about the "every meal for a day" thing, I'll give her the benefit of the doubt, mainly because it doesn't much matter.

There follows the actual dishes prepared, with hunger-inducing photographs.

I just have one thing to add: absinthe.

The first time I tried absinthe was at a Moroccan-themed bar here in my town. I forget the exact ritual they went through, but fire was involved. And I liked it enough to go buy absinthe and try it myself. But the serving of absinthe, with or without fire, is kind of finicky. Sure, you can drink it straight, like other liqueurs, but, like some other liqueurs, it's not really meant to be straight.

At the very least, the serving of absinthe involves ice water and sugar. Generally, you pour the absinthe into a specialty glass and then use some contraption to let the ice water drip slowly into it over a sugar cube.

As I am, above all, a science nerd, I decided to compare flaming absinthe to not-flaming absinthe. Of course, I used the same absinthe, same water source (my kitchen sink) and the same kind of sugar (Domino's brown sugar cubes), because science is all about controlling variables.

The result? In my not-humble opinion, the one without fire had the superior flavor. It was also, I can only assume, more potent because the alcohol hadn't burned off.

However... the flaming absinthe was just more fun.

6 Like • Comment • View 1 comment

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