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Monday, Oct. 7, 2024

5:23am EDT

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Complex Numbers

by Travelin' 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:

Cackling QPdoll

about 21 hours ago
In response to "Like a Bosteels"

The glasses are cool. It's no wonder they walk off.

1 Like

Travelin' Waltz

a day ago
In response to "It Was Just Waffle"

Annette

, WakeUpAndLive️🦇Elf'sSpell

- there's also the Hergé Museum.

2 Like

Cackling QPdoll

a day ago
In response to "It Was Just Waffle"

I was so tense with you reading about your adventure. It's good the tour was rescheduled, but your legs lost out in the meantime. I'm sure returning to the hotel was so much fun! Glad you're having a good time. Well, despite the cobblestones anyway.

1 Like

Wordsmitty ✍️

Oct 5, 2024 at 3:49am
In response to "It Was Just Waffle"

Mmmm. Chocolate (the good stuff (not american))

I ordered food once with a computer tablet mounted on the table in Japan. Real people brought the food though. No robots. It was a Denny's. No I didn't get pancakes.

Computer and instructions to order food at Denny's in Japan

1 Like

WakeUpAndLive️🦇Elf'sSpell

Oct 5, 2024 at 2:47am
In response to "It Was Just Waffle"

Travelin' Waltz

and Annette

There is a giant wall painting (64 mtrs2)of TinTin in the train station South station (Zuidstation) entrance Hortaplein (Horta square) in Brussels. The statue of TinTin is in a little town Ukkel, unfortunately.

1 Like

Annette

Oct 5, 2024 at 1:35am
In response to "It Was Just Waffle"

French fries are really Belgian fries. Make sure to try some.

Do they have any Tintin statues?

Lazy Writer est 4/24/2008

Oct 4, 2024 at 12:28pm
In response to "Coats Do What Now?"

I do some want to make this trip! I hope you are having a ball!

WakeUpAndLive️🦇Elf'sSpell

Oct 4, 2024 at 3:53am
In response to "Coats Do What Now?"

When I was a couple of times in France I found the language difficult because of the speed at which they talk. With my limited (high school) knowledge of French. And the locals were not always that friendly. Have you met any of those? Enjoy Belgium, hm...I am not sure if you will like that country. We'll see. But I think the beer tour will be to your taste.

1 Like

Kåre Enga in Montana

Oct 3, 2024 at 3:38pm
In response to "Owl Miss This Place"

I like wandering. Yes, I may miss a lot but it's my dime and my time. I don't have a checklist.

I think I would like Dijon.

1 Like

Kåre Enga in Montana

Oct 3, 2024 at 3:33pm
In response to "Enough With the Rain, Already"

I believe I understand the umbrella (pardon my French) and the sentiments. I like rain though. Just not relentless heavy rain that led to the floods in Appalachia.

Keeping up with young folks ... realized I had gotten old 5 years ago in Tainan. I couldn't keep up.

It would make sense that the local wines, cheese, cured meats would compliment each other. Staying local gives a local experience. If you MUST have a MacDonalds burger and a Bud Light everywhere you go it defeats the purpose of traveling, imho.

1 Like

October 7, 2024 at 2:31am

#1077880

Brewgge

Compared to the previous couple of days, yesterday was easy: Walk around Bruges, drink beers.

The rescheduled private Bruges beer tour happened, and the Ukrainian guide introduced me to more beer. We started at the Beer Museum, and yes, there is a Beer Museum in Bruges and it contains a taphouse. You might think, "But Waltz, haven't you tried them all already?" No. No, I have not. I haven't even tried all the ones that make it to the US, let alone the good stuff they keep to themselves here.

Tant de bières, si peu de temps.

There exist over 400 breweries here. Most of them produce more than one brew. And things keep changing, so I don't think I could try all of them even if I wanted to (which I do). It's enough that I have the impossible dream of visiting every brewery in the US (we're up to around 10,000, but we keep losing and gaining them).

The ones I did try, though, were generally good. There are some styles I just don't enjoy as much, so mostly, it's a matter of personal taste, not a reflection of actual quality of product.

In addition to this, I fulfilled a long-standing fuck-it list item and visited the Torture Museum

here. What they don't tell you at the link there (Atlas Obscura) is that you have to walk down a flight of dark, ominous stairs to get to the museum in the basement, and that there's a cheery café on the ground floor which doesn't seem to have any connection to the museum... or does it?

Unlike with beer, I have no desire or inclination to try all the devices in the museum. Still, it was a good reminder that humans can really suck, sometimes.

And sometimes we can do great things, like create beer. Pictured: La Corne du Bois des Pendus, another beer with unique glassware, on a table on a terrace by a canal.

2 Like • Comment

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