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Thursday, Nov. 14, 2024

1:44am 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:

Brandiwyn🎶

a day ago
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.

Aiva Raine

Nov 5, 2024 at 3:03pm
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

Nov 5, 2024 at 2:55pm
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

September 26, 2024 at 3:45am

#1077301

Two Castles and a Cave

My schedule yesterday was pretty much: go on a tour.

Now, I've been trying really, really hard not to make a joke about Tours tours. You have no idea how difficult that is for me. It's sitting right there; how can I not pick it up?

I've been unable to find a reliable etymology for the city's name, for which, incidentally, the s is silent. Wiki says there's a "popular folk etymology" that it's named after a Roman named Turonus, nephew of Brutus (but not that Brutus). I've long thought that it comes from the French word that translates as "tower" in English, as in La Tour Eiffel. Far as I can tell, though, there aren't any significant towers here. Perhaps there were, once. Hell if I know.

The point is, I'm trying really, really hard not to make a pun about it.

What I do know is that it's wine country. Pretty much everyone has heard of Bordeaux to the west and Burgundy to the east, as well as Champagne, which is located between Paris and Belgium. I think the Loire valley, or Val de Loire, is not quite as well-known internationally, though it absolutely should be.

Getting back to what I originally set out to write, the travel agent had arranged a small group tour to run outside the city. By "small group," I mean there ended up being three of us. Continuing my run of coincidences, the other two were a couple from Fairfax, in northern Virginia. The guide was this small French woman who'd prepared an entire booklet of illustrations, some quite amusing.

First stop: Château de Chenonceau. I'd never heard of it before this trip, but apparently it's the second most visited castle in France, after Versailles. The really interesting thing about it is that it straddles a river.

Like, the brief version is: someone built a castle on the bank of the river Cher. Later, wanting an easy way to get to the other bank, they built a bridge from the castle to the other side of the river. And still later, a massive three-story structure got built atop the bridge. The day was rainy and nasty, and I didn't get any really good pics of the outside, but you can see the bridge-castle here.

I was starting to gain an understanding of what might have led the French peasants to revolt in the 18th century.

Then we went to a cave.

Not just any cave, of course, but a wine cave. And yes, of course, a wine tasting was involved, complete with a brief tasting class led by a sommelier who supposedly passed on some of the "secrets" of his profession. I mean, they're not secrets anymore, now that I know them. What are they? I'm not telling.

After eating lunch (with wine) just outside the cave, we went on to the next castle: Chambord.

Sadly, it had nothing to do with the berry liqueur called Chambord. Or, really, with any booze. It was another example of the excesses of the French nobility, further deepening my understanding of why the guillotine was invented.

Still raining (which the sommelier had assured us was a Really Bad Thing for this year's grape harvest, because apparently it hardly ever rains in the Val de Loire in early autumn, and I didn't point out that this was probably my fault because I've been known to end droughts in California just by visiting the place), so again, none of my photos are very good and I'll defer once again to Wikipedia.

So, with all the crappy weather, what pic from this tour can I share? Oh, I know! This dude was hanging out in a stable at Château de Chambord. You might need to enlarge it, but I promise the white streak on the right side belongs to a horse.

6 Like • Comment • View 3 comments

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