Complex Numbers (Book)

Blog Calendar

◄ July ► 2019
S	M	T	W	T	F	S
	1	2	3	4	5	6
7	8	9	10	11	12	13
14	15	16	17	18	19	20
21	22	23	24	25	26	27
28	29	30	31
Archive				RSS

About This Author

Contact Me

Come closer.

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/

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:

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

Turkey DrumStik

Nov 6, 2024 at 10:22am
In response to "Lo!"

Not gonna lie I need the holiday season chatter.

July 1, 2019 at 12:11am

#961842

Road Trip!

It’s summer here in the US, the perfect season for a road trip! In your blog today, plan your ideal road trip. Where would you go and who would you go with?

This is something I do fairly regularly.

For anyone just tuning in, I've documented some of my road trips on my offsite blog.

My parameters vary. I've said this before, but the first time I did this, I got it in my head to travel from the easternmost point in the continental US (Lubec, Maine) to the westernmost point (an empty spit of land on the coast of Washington State). One time, I just picked three destinations at random - more on the random thing later. Whatever the route, my ideal road trip stays off of interstates, meanders somewhat, and gives me plenty of time to see the sights.

For various reasons - perhaps I just like to live on the edge - I tend to travel in late fall and winter, not summer. The obvious hazard is that sometimes it snows. One time, I got caught up in a blizzard that stretched all the way across New Mexico from the Arizona border to Amarillo, Texas. That time, I stayed on an interstate. On another notable occasion, I nearly got stuck in an 8 foot drift in Vermont. Fortunately, I was near Ben & Jerry's at the time. Also fortunately, "nearly" means "didn't."

The not-so-obvious hazards are that more places are closed, especially in the northern states, and some roads are seasonally barricaded.

There used to be a website that emulated a dart board thrown at a map. You set parameters and it picked a random destination within those parameters. Sometimes, the spot would be in the ocean, or the middle of a lake, or, in one memorable case, a place in the middle of Nevada, far from any highway, with a lot of guys with guns standing around. But usually, you can just see which points are invalid, and try again. Unfortunately, that site no longer functions, because of changes Google made to Maps.

Sometimes, Google pisses me off. Not enough to swap my Android for an Apple, though.

The other issue with random destinations on that scale is that the code isn't always transparent. All other things being equal, you can't just return a random set of latitude and longitude coordinates and call it truly random; those points aren't evenly distributed. There's a notable increase in density of possible targets the further north you go, as the longitude lines converge. I don't like that. I want the same chance at every spot.

The last time I picked a random destination, it was via a site that returns random ZIP codes in the US. Ended up in a suburb of Boston that time.

But the question was not about my past adventures, but about my ideal road trip. So let me tell you about my ideal road trip.

At last count, there were nearly 6500 craft breweries in the United States. The vast majority of these are local microbreweries. A few are regional. Even fewer are set up to produce the kind of volume it takes to ship nationwide. And my dream is to visit every one of them.

This is not easy, especially since it becomes a Sisyphean task: every week, on average, we gain two craft breweries and lose one. Approximately. So even if I could visit all of them, some would be gone by the time I got to them, and others would spring up in my wake and I'd be forced to turn around and go back to places I've already been. And that's not even counting the simple math that even if I visited ten of them each day, it would take nearly two years. Possibly more, since some are open on different days than others. My personal record is 12 microbreweries in one day, and that was in Asheville, NC, which has more microbreweries than hot yoga studios - and that's saying something.

But... everyone needs a goal in life, and this is mine.

The biggest problem is this: I'm not just visiting to visit; I want to sample their wares. While most samples are small and have little effect, visiting more than one or two in a day makes it so I can't legally drive to the next one. So what I need is a full-time designated driver. This is difficult, because very few people like me enough to hang out with me for that long, and those few who do would want to participate in the goal, thus negating their usefulness as a DD.

This answers the other part of the prompt: who would go with me? It's not like I can advertise on Craigslist, or as I like to call it, Scamlist. I need a friend who has nothing better to do. I'm even willing to pay them.

Self-driving cars can't get here fast enough, as far as I'm concerned.

Then there's the problem of lodging. I don't trust AirBnB worth a damn, and motels get expensive; these expenses add up. Cheaper in the long run to get an RV. But then you run into another problem: Any RV big enough to house two people comfortably can't find parking at most destinations, while any RV small enough to fit into standard parking spaces will lead to personality clashes.

Meanwhile, I'll just keep doing what I'm doing, which is visiting breweries whenever I can, using Uber or Lyft to get me there from a central location.

But I can't help thinking that there's gotta be a way...

1 Like • Comment • View 2 comments

© Copyright 2024 Robert Waltz (UN: cathartes02 at Writing.Com). All rights reserved.
Robert Waltz has granted InkSpot.Com, its affiliates and its syndicates non-exclusive rights to display this work.