Complex Numbers (Book)

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Complex Numbers

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/

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Show Recent Comments

10 Most Recent Blog Comments:

Turkey DrumStik

about 5 hours 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

December 2, 2018 at 12:31am

#946684

Artificial Creativity

You will be replaced by a machine.

Yes, you. Well, unless you retire or croak before the machine gets a chance. Many replacements have already happened (assembly line workers, cashiers), and many more are on the way (see: autonomous vehicles).

But maybe you never considered that a computer could write better than you can. Not yet, but they're working on it.

https://getpocket.com/explore/item/the-six-main-arcs-in-storytelling-as-identifi...

Until that happens, there are some pretty good takeaways in the above link for us soon-to-be obsolete human writers:

A story's emotional arc can be used to assist in plotting the narrative. The article identifies several of these arcs, and hints at the idea of nesting them within a longer story. We can use this consciously, whereas I think a lot of writers do it unconsciously.

Be aware of which words people find to be "happy" or "unhappy," which may not correspond to your own opinion. For example, "laughter" is in the list of happy words, but because of unresolved issues from childhood, it's doesn't register that way for me.

Have a look at the "Rags to Riches" archetype graph. It's maybe 2/3 down the page. Well, I was expecting a kind of ascending line; I mean, that's the implication, right? You're poor, which sucks; good shit happens, and then you're rich, which is awesome. But no, instead we have something resembling a partial sine curve, right? Curves down, bottoms out near the beginning, rises more or less smoothly to a peak... but the peak is not at the end; there's a downturn right before the end. It's implying that a rags-to-riches story can't just stop at the high point; there has to be, perhaps, some acknowledgement that everything's not as awesome as we'd hope. I mean, that drop-off at the end is pretty sharp.

Going back to near the beginning of the article, yeah, I'm gonna part with ol' Kurt on his opinion of the similarity between the Cinderella narrative and the Bible. I mean, I think he's right about the Cinderella plot shape, that works, but to apply that to the Bible you pretty much have three chapters of Genesis, then you fall into a great big hole, and then you don't climb back out until you get to the New Testament. It ignores the shapes of all the stories in between, such as the whole "escape from Egypt" and "Joshua kills half the Canaanites and enslaves the rest" bits. Besides, the Fall was the best thing that ever happened to us. Or, you know, it would be if I took the story seriously.

I want to see this work replicated independently. I'm not sure there wasn't some kind of selection or other bias.

Anyway, thought I'd link something that's actually about writing, for once. Not that it'll do me any good. I'm still too lazy to work on my own stories. At least I can get these entries done.

2 Like • Comment • View 3 comments

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