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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:

tj-turkey-jobble-jobble-hard-J

about 13 hours ago
In response to "Revisited: "A Frank Discussion""

I became disgruntled with meat sold in local grocery stores; half the weight is water, the taste is bland, and it's "use by" date is usually one day away. I found a small town butcher/locker plant that sells locally raised meats and buy in bulk so it's actually fresher, cheaper, and better tasting. Recently, I decided to try my hand at making our own sausage as well. It's a bit of work, but I think it's worth the trouble.

1 Like

Turkey DrumStik

a day 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

August 22, 2023 at 10:23am

#1054434

Boregon Trail

After that bit of head-stretching yesterday, here's something a little closer to home:

Top 10 States Voted as the Most Boring to Visit in the U.S. by Americans

Admittedly, "boring" is subjective. By what criteria? Are your expectations too high? Are you a teenager and find everything boring? Do you live in a big city and wish someone would mug you more often? Well, I've been to all but three states in the US, so I obviously have my own thoughts on this list.

1. Nebraska

According to the next traveler Nebraska is the most boring state in America, and they stated that there is nothing that would motivate them to visit again.

And naturally, this is one of the three states I haven't been to. But assuming it's an average of Kansas and South Dakota, sure, traveling across it probably induces boredom..

They seemed to believe that the state lacked excitement and allure compared to other states. Many fellow Americans agreed, and another stated, “There is nothing but cornfields.”

What? You don't like to eat? You don't like to drink bourbon? You have some deep-seated hatred of farming culture, despite, you know, depending upon it?

I can believe Nebraska is boring to drive through. However, statements such as these say more about the urban ennui of the statement-makers than about the subject matter.

2. Delaware

Oh, come on. You just included this one so people couldn't go "that's why they call them flyover states."

The commenter wrote that all three counties of it are nothing but an elaborate tax dodge masquerading as a state.

That bit is legitimately funny. Like, three counties in a trench coat pretending to be a state.

3. Kansas

Yeah, well, see above.

4. North Dakota

I admit I had to play little games with myself while driving across North Dakota in order to alleviate the boredom, but the state has a unique beauty to it. That probably extends across the border into southern Manitoba and Saskatchewan, but I have no first-hand evidence of this.

The worst thing about ND, from my perspective, was trying to find a place to crash. There was an oil boom going on while I was there, and everything was full.

5. Iowa

I... kinda love Iowa. Not the politics or anything, but the scenery. It's not nearly as flat, or as uninteresting, as people make it out to be. Maybe this is because I don't use interstates on my road trips.

6. Ohio

Despite being the birthplace of many famous individuals, such as the Wright Brothers and Neil Armstrong, this traveler believes that Ohio is lackluster regarding things to do and see. The user argues that Ohio is simply a state to pass through rather than a destination worth stopping at. They acknowledge Ohio’s impressive record of producing more astronauts than any other state but ultimately deems it insufficient in excitement and interest.

Oh, fuck right off with that. You want excitement? Stay in NYC and L.A., and leave the rest of us alone. We don't want you, either.

On the other hand, it could be that so many astronauts come from Ohio because they felt a deep-seated desire to get as far away from the state as possible...

I won't quote the rest, other than to say that one of them, Michigan, is also one I haven't yet visited. (The third one I'm missing is Alaska.) But it's clear to me that some of these responders have no sense of adventure, or beauty. Despite my gripes above about driving across certain plains states, fact is, I'd do it again. Sure, I have a much higher tolerance for what others consider boring, but in practice, it's a beautiful country with lots of hidden gems scattered across it. I'd do it all again.

Hell, even getting stranded in South Dakota a couple of years back ended up being quite the adventure.

In short, if you find one of these states boring in general, that's on you, not the state.

3 Like • Comment • View 3 comments

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