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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:

Write_Mikey_Write!

a day ago
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

a day ago
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

Turkey DrumStik

Nov 6, 2024 at 10:22am
In response to "Lo!"

Not gonna lie I need the holiday season chatter.

October 9, 2021 at 12:13am

#1018996

The Sioux Chef

Back for another "Journalistic Intentions"

[18+] entry today.

Sean Sherman

Gotta love a good pun, which is, by definition, also a bad pun. A bad pun that alliterates is even better. A bad pun combined with a quadruple alliteration (or close enough)? Gold. Sioux Chef, Sean Sherman. Come on. You gotta check out the link for that alone.

When I was in Minneapolis around the beginning of July, wandering around the riverfront in the vicinity of the waterfall and lock (once a civil engineer, always a civil engineer, and massive public works projects intrigue me), I discovered the restaurant, Owamni, featured in the above link.

Okay... "discovered" is a bad word in this context and obviously I should be shunned forever for daring to use it. It's kind of like the faux pas I made as I was checking into a hotel in Kayenta, Arizona, several years ago. Kayenta is in the Navajo nation in the far north of the state; tourists with an inexplicable need to be *shudder* outdoors use it as a gateway to all the cool shit in southern Utah, whereas I was just passing through. I'd planned the stop in advance, so I staggered into the hotel (I think it was a Holiday Inn Express, or maybe Hampton; one of those franchise chains) under my load of luggage, stumbled up to the counter, and said to the nice lady, "Yeah, hi, I have a reservation..." And immediately regretted it.

She didn't kick me out. This hotel, it turned out, included a restaurant run by a Navajo chef, and thus was I introduced, for the first time, to the absolute delight that is Navajo frybread.

The pre-invasion people living in North America were, of course, quite diverse, as is the country's climate and terrain. Without the benefit (and don't misunderstand me; it is actually a benefit) of international trade, people kind of have to use what food sources are available wherever they happen to be. This was, of course, true of people everywhere in the world, but today I'm talking specifically about the continent I live on.

But I also know this: humans are humans, wherever they are. When I was growing up, I got full-on indoctrinated into the whole "Indians lived off the land in harmony with nature" schtick. While there's probably some degree of truth in that, it's kind of idealist and dehumanizing all at the same time. Humans migrate, and we tend to take with us some of the food from wherever we came from. And as we saw several entries back, agriculture was most definitely A Thing in North America before the Europeans got here.

In any case, the point is, what the Sioux or Dakota people ate on the Northern plains would have been different from what the southern desert people ate. I mean, duh. It's kind of like how, now, you can't eat anywhere in New Mexico without being asked "red or green chili?" whereas in Minnesota, the idea of any sauce more powerful than mayonnaise is met with absolute shock and horror (yeah, yeah, I know, not all Minnesotans, whatever).

So you can imagine how thrilled I was to see the sign for Owamni there on the bank of the Mississippi, and how utterly devastated I was to find that it had not yet opened.

I think it's open now, but of course I'm not in Minnesota.

I did get to tour the river lock, though, and that was cool.

4 Like • Comment • View 5 comments

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