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Saturday, Nov. 16, 2024

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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

5 minutes 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!

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

May 26, 2024 at 8:30am

#1071700

Revisited: "Big Bang"

Way back in May of 2008, I did an early version of my "comment on a link" thing, combined with a mini-rant: "Big Bang"

As that was 16 years ago (I can math), it's not surprising that the link is no longer functional, but I think we can all get the general idea: someone found a stash of expired fireworks, and authorities decided to blow them up using plastic explosive.

Looking back on this now, I'd still take the attitude that they only did it because they could. From what I've heard since then, the proper and safe way to dispose of stale firebangers is to immerse them in water and let them soak for a good long time. But where's the fun in being proper and safe? I may be older and (arguably) wiser now than I was when I found that link, and I may have turned into the neighbor who moans about other people in the neighborhood illegally making booms and whistles around every Fourth of July, but that doesn't mean there isn't, somewhere inside me, Kid Me, who would definitely have wanted to see a bunch of old fireworks get blasted by 30 pounds of C-4.

The only difference is nowadays, I'd be more careful about where I did so.

As for the rant, it was about Mother's Day, which apparently was the day of that entry:

I thought about writing something about Mothers' Day here, but what's the point?

This year, I completely ignored it.

My mom died nine years ago this summer...

Obviously, that's 25 years ago now. That's a longer span of time than I spent living with her.

...and why the hell is there a special day reserved for people who managed to reproduce?

In fairness, there's a special day reserved for just about anything. Today, for example, is Sally Ride Day,

celebrating the birthday and legacy of the first female US astronaut (and who had one of the most awesome names in the history of names, thanks to a certain Wilson Pickett song). Now, there's a woman who accomplished something.

Hell, hamsters can do that. How about reserving a day for those who care enough about the planet and its other life forms that we did not breed like rabbits?

Note to self: stop mixing rodent and lagomorph metaphors.

And that goes double for Father's Day.

Lest anyone labor under the misconception that my rant was reserved for females alone.

Of course, at the end of the entry, I clarified that the whole rant was satire:

Oh, about the first paragraph? I'm just kidding. Mothers - and fathers - should definitely be acknowledged, not for breeding, but for bringing you up right.

If, that is, they did so.

About the only thing I truly regret about that long-ago entry was not being more explicit in tying the "Big Bang" of the fireworks disposal with the "Big Bang" usually associated with the conception of offspring. It's even possible that I didn't make the connection back then, but now, being older and (arguably) more foolish, it jumped right out at me like a rabbit. Or a hamster.

2 Like • Comment

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