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Wednesday, Nov. 13, 2024

1:07am 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🎶

about 14 hours 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 2, 2024 at 1:35am

#1076064

To Live Until I Die

"Blog Week Birthday Bastion 2024"

[13+] by WakeUpAndLive~doingNaNo'24

Prompt 2. Sept 2.
Tell us about an earthshaking Life-or-Death situation in your life. What happened, how did it change you, if at all?

I've been close to death three times that I know of, each time from some medical issue.

I say "that I know of," because who knows what might have happened had I crossed a street a few seconds later, or decided to go out instead of staying home?

Thing is, none of those instances were particularly "earthshaking." For a human over the age of, maybe, 3 or 4, being alive means living with knowledge of your own mortality, even if only in abstract terms. As better writers than me have noted, death is one of the very few certainties, along with taxes and construction on the Capital Beltway. Doesn't make it easier to contemplate, maybe, but you know it's coming.

And with age comes even deeper knowledge of the inevitability of drawing one's final breath. You've lost many pets, if you're lucky enough to have had pets. You've lost family. Maybe you've lost friends to the Reaper's scythe. Or, like me, you watch your parents slowly decline into husks of their former selves, to the point where death becomes a release and a relief, not something to be feared. It creeps closer and closer, as sure as getting honked at in Manhattan. The only unknown is: how are you going to handle the knowledge?

Back when Facebook was new and shiny, I had an account there (still do, because I can't get into the damn thing to close my account, but that's not really relevant) and I, like many people, became curious about what people I knew long ago were up to. I found a mutual friend of a high school girlfriend, whom I asked about—not trying to start anything back up, but like I said, just curiosity. "Oh, she died a few years ago," the mutual friend told me.

Apparently, she'd just gotten back from her honeymoon and was in great spirits, looking forward to her new life, when she collapsed on a sidewalk from an undiagnosed congenital heart condition. She was in her early 30s. Her twin brother, who, somewhat predictably, never much liked me, got checked out; turns out he had the same condition, but knowing about it, the docs were able to treat it. Last I heard, he was still kicking. I even ran across his name in a news story once, a few years back.

I may be getting some of the details wrong, because this was long ago, and her death even longer ago, but the result remains the same: that's most likely when it really hit me that anyone can die of anything at any time. Sure, I'd known that intellectually, but that was probably the moment when I felt it in my gut. What changed my perception, at least to some degree, was facing not the prospect of my own death, but getting hit by the news of the death of someone my own age I'd once cared about.

Some people deal by trying everything they can to extend their life. I can understand that, though that's not me. Other people deal by deliberately trying to shorten it. That's not me, either. Still others cling to the belief that there's a life after death, that their consciousness will, through supernatural means, survive their body's demise. While I'm not here to disparage anyone's closely held beliefs, I couldn't take comfort in that; one of the many things I'd find scarier than death would be eternal life.

No, between watching my parents decline and die, and hearing about my former girlfriend, the only thing that makes any kind sense to me is to live while I'm still alive. Sometimes, that means doing things that have been shown to reduce one's life span, but that's not why I do them. I do anything I do for one overwhelming reason:

I fucking feel like it.

And that, folks, is why I plan to be in France three weeks from now: because I feel like it.

I could die tonight. Or on the trip. Or 20 years from now, or anytime in between. But I lived first.

Life's too short to drink the cheap stuff.

You wanna live until
You die alone and will
And I can fly alone at will
I'm not so far below
I'll live beneath your sky
With tainted eyes
I've made my mind
To live until I die

Let's do this again. We get to give out a free Merit Badge every day this week. Want one? Anyone who comments here before 11:30 pm WDC time today could get today's. (I'll need that extra half-hour to pick a winner and send the badge before midnight.)

To clarify:

When I say "comment," I mean comment. Not review. Though reviews are always welcome.

I also mean "here," not on the newsfeed post.

MB recipient will be chosen at random.

Maximum of one MB per commenter for the week.

If I don't get comments, I'll pick a previous commenter, and maybe not at random.

The MB will be the one I commissioned two years ago, "Complexity," which is a publicly available MB.

I appreciate all comments; this is just a little incentive.

5 Like • Comment • View 7 comments

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