Hidden Things in Map of Roshar?

[happyman]

Here's what I consider a pretty simple explanation of the Julia set.

 

Take a mathematical function f(x). Choose a random number x₀, from the domain of that function. Find out what f(x₀) is (let's say f(x₀) = x₁), then feed it back into f. Find out what f(x₁) is. Feed that back into f to get x₂. Repeat to infinity for all possible initial numbers x₀. All the original numbers, or seeds, that give you a sequence x₀, x₁, x₂, x₃, ... of fairly similar numbers are something we'll call "prisoner set of f;" all the seeds that give you erratic sequences x₀, x₁, x₂, x₃, ... will be the "escapee set of f." Well, the Julia set of the function f is the set of those seeds that form the border between the prisoner set and the escapee set.

 

Here, let me edit with an example.

 

---

John Carroll University has a really nice vignette on Julia sets, so I am going to use their example - it's clear enough and it saves me some work.

 

Let's take our function to be f(x) = x² - 0.5. We now need to look at all the possible x₀ we could feed into this function - which, in this case, means all (real and imaginary!) numbers. To illustrate the prisoner and escapee sets, however, we'll only look at a couple of numbers.

 

If we take x₀ = 0 (0 is always nice, makes math easy), we get the following sequence x₀, x₁, x₂, x₃, ... :

x₀ = 0

x₁ = f(x₀) = f(0) = - 0.5

x₂ = f(x₁) = f(-0.5) = - 0.75

x₃ = f(x₂) = f(-0.75) = 0.0625

...

If we continue this, we'll see that the numbers we get never move too far away from the original x₀ = 0. This means 0 is part of our prisoner set.

 

Now, we take a different x₀, let's say 2. Do the same thing:

x₀ = 2

x₁ = f(x₀) = f(2) = 3.5

x₂ = f(x₁) = f(3.5) = 11.75

x₃ = f(x₂) = f(11.75) = 137.563

...

Unlike the case where x₀ = 0, here it's easy to see that the numbers will continue growing (exponentially). This kind of behavior means x₀ = 2 is a part of the escapee set of f. It's also easy to see that any number greater than 2 will also be a part of the escapee set, by the way.

 

Now all you need to do is repeat the same thing for all the numbers (keep in mind, the example I gave doesn't even touch the imaginary numbers / components), plot them, see which one(s) form a boundary between prisoner and escapee sets, and voilà - Julia set!

 

If you are curious, here's how the Julia set of our example function looks like:

 

 

Good, very good explanation, and upvote for writing it.

 

I would note, thought, that I had a pretty easy time creating a function for which this explanation isn't sufficient by itself (I deliberately set out to do so).  It's not relevant for this thread, but if any one out there is looking deeper, don't feel you're going crazy if the real mathematicians start using terms much more obscure but technically accurate.

 

Mind, I think that any explanation should start with this explanation as a motivation.  Reading the Wikipedia articles on Julia sets was far from useful.

[GreyPilgrim]

I must say, great job, guys! This thread is amazing and terrifying at the same time. It is basically 17th Shard condenses into a single thread. This thread represents everything this site is: a sanctuary for the many insane fans of Brandon Sanderson and all of their differences. Everyone here has something great about them, and this lets us all shine!

It is also threads like this that must terrify Brandon. That anyone is willing to this in-depth into his works is kind of frightening. We are like a fanatic cult, more than a simple fan base.

[Kobold King]

I must say, great job, guys! This thread is amazing and terrifying at the same time. It is basically 17th Shard condenses into a single thread. This thread represents everything this site is: a sanctuary for the many insane fans of Brandon Sanderson and all of their differences. Everyone here has something great about them, and this lets us all shine!

It is also threads like this that must terrify Brandon. That anyone is willing to this in-depth into his works is kind of frightening. We are like a fanatic cult, more than a simple fan base.

 

"Emily! The Sharders are being crazy-obsessed again."

 

"Storms. I'll set the burglar alarm so they can't sneak in for the Stones Unhallowed outline. You stand in the doorway and RAFO everything they throw at you."

[deadlyDomino]

So if i understand correctly, the Julia set is chaotic in contrast to the Fatou set, which is ordered.

 

 

...is there any chance that one of the other landmasses/planets/Shadesmar locations in the Cosmere corresponds to a Fatou set, thus indicating it to be either diametrically opposed or linked to Roshar?

 

 

And just when i thought I'd STOPPED going mad over this problem.

[+rhaiynebow]

Would one of you guys be willing to summarize what was found so I can be lazy and not have to go through 34 pages of posts to find the tidbit of info? And in English please, not Mathematics  I read all the posts on this page and my brain just automatically went into auto pilot as soon as it saw algebraic type equations and graphs n stuff LOL. I am SOOOOOO not a math person!!

 

Thank you, thank you, thank you in advance!!

[Maffu17]

 

I must say, great job, guys! This thread is amazing and terrifying at the same time. It is basically 17th Shard condenses into a single thread. This thread represents everything this site is: a sanctuary for the many insane fans of Brandon Sanderson and all of their differences. Everyone here has something great about them, and this lets us all shine!

It is also threads like this that must terrify Brandon. That anyone is willing to this in-depth into his works is kind of frightening. We are like a fanatic cult, more than a simple fan base.

 

 The most impressive thing is Sanderson's creations are inhumanly brilliant. I don't even have the words to express exactly what it is that impresses me. He puts so much thought and effort into his work it's amazing. He threads together his stories like a master weaver, so that here we are months and years later finding new treasures with every new warp or weft we investigate. Then we find that the tapestry of each book is but a smaller part of something larger and our minds get blown anew. His dedication to the social aspects of his job, the interactions with fans seem to give him genuine pleasure. The way he adapts to the levels of his readership from Alcatraz through to the Stormlight Archive. The moments of realization you get when everything starts to fall into place and your mind races backwards and ahead at the same time trying to put everything together, so each book culminates in a race between your eyes and your brain that doesn't even end after the pages run out, the first lines of tWoA "I write these words in steel..." you know he writes with a cheeky grin on his face every time he drops a clue surreptitiously into an innocuous paragraph ("is it the heart of a beetle?"). The speed at which he does all this, releasing books ceaselessly all the while looking at adaptations into other media without compromising on quality while Rothfuss, Martin and Brett plod along with a book every few years (if we're lucky) is astounding. I want to talk about the characters like Jasnah, Marsh, Rashek, Kaladin but where to even begin, their depth, growth and realism is staggering. 

 

I don't like to bad mouth other authors but the truth is that readers have evolved, we're much harder to please than we used to be and many writers struggle to even escape the stagnated Hero's Journey or Monomyth. Many create original and entertaining stories which can entertain as long as you don't ask too many questions. A handful whisk us away into believable worlds populated with characters we care about, and if they manage to sustain the pace through to completion they are lauded as masters in their field. However, atop them stands one man, waving a Shardpen and pushing the boundaries of storytelling into dimensions we didn't even know were there.

 

Seriously I've been at this post almost 2 hours and i'm just struggling to convey all the awesomeness into words, if someone with more eloquence than I would care to explain what so special about Brandon I'd love to read what I really mean, if you know what I mean.

[ccstat]

Would one of you guys be willing to summarize what was found so I can be lazy and not have to go through 34 pages of posts to find the tidbit of info? And in English please, not Mathematics  I read all the posts on this page and my brain just automatically went into auto pilot as soon as it saw algebraic type equations and graphs n stuff LOL. I am SOOOOOO not a math person!!

 

Thank you, thank you, thank you in advance!!

If you go back to the opening post, Rshara has updated it with both a summary of all 34 pages of the thread (courtesy of Veil) and the "actual answer" discovered by Veil and Jensen. Essentially, there is a mathematical thing called a Julia set, of which Argent gives a good explanation. One of these generates a graph that looks identical to the map of Roshar. 

(It's a bit more complicated than that, since the graph is actually 4-dimensional, and the discussion on the previous page was about how to describe which portion of the graph resembles Roshar).

[Delightful]

@Maffu17. A Shardpen! Of course! That explains *everything*!

[+rhaiynebow]

@ccstat - THANK YOU!!

[Maffu17]

@Maffu17. A Shardpen! Of course! That explains *everything*!

 

oh wow you linked my post in your sig thingy! I'm delightfully flattered

[Kobold King]

oh wow you linked my post in your sig thingy! I'm delightfully flattered

 

Delightfully flattered... there is no way that wasn't a deliberate pun. Take an upvote and convey yourself to the pun thread, we need more men like you.

[Maffu17]

I wanted to say I was touched and got a warm feeling inside and it made me smile with a little bit of pride, and then my brain overrode my fingers because I couldn't think of a none-sappy way of saying that and it made me do the pun to cover my embarrassment but also still try to convey my pleasure.... Brains.... can't live with 'em...

[BreathTaker]

 Brains.... can't live with 'em...

 

That's it, that's literally the end of the saying I can't believe how easily amused I am. I have been online for about ten minutes today and I have already laughed heartily at the probably FIVE posts that I read here. UPVOTES FOR THE LOT O' YE!!

Fatal error: Allowed memory size of 387973120 bytes exhausted (tried to allocate 416749872 bytes) in Unknown on line 0

[Delightful]

oh wow you linked my post in your sig thingy! I'm delightfully flattered

No worries It just makes so much sense! I'm delighted that seems to have made your day!

(and I.....totally reused your pun because.....excuse my ignorance, is Maffu a word?)

I agree with Kobold King, you should go check out the pun thread

When you said 

 

 

atop them stands one man, waving a Shardpen and pushing the boundaries of storytelling into dimensions we didn't even know were there.

I just had this image of Brandon standing on a desk amid towering piles of papers that literally cover the desk, the floors,and the mahogany bookshelves behind him, dramatically holding up a glowing blue pen with stories pouring out the end of it. And that's just pure awesome. So thank you.

Edited April 27, 2014 by Delightful

[Swimmingly]

Brandon reading this:

Oh god, I wish it was that easy...

[Delightful]

Brandon reading this:

Oh god, I wish it was that easy...

Maybe it is. We would never know. 

[Kobold King]

Brandon reading this:

Oh god, I wish it was that easy...

 

Shardpens can be tricky. If you drop it, you've got to wait ten heartbeats before you can start writing again. And if you absentmindedly chew on the tip, you can accidentally sever the soul from your lower jaw.

[Shaggai]

Brandon reading this:

Oh god, I wish it was that easy...

He's probably thinking something along the lines of "Good. They still don't realize I'm a Zinc compounder."

[Swimmingly]

Well, if Brandon's using a magic system, I'm sure he hasn't written about it. After all, no one character knows everything, and if he'd written about the magic system he was using, he'd be a character that knew everything about it. The universe would collide with the Cosmere, and physics would fail as Investiture migrated to areas of low pressure.

[Psymon]

I haven't read all the thread yet, stupid finals that i have to study for!, but has anyone else wondered what the rivers on Roshar would translate to in Shadesmar?

[Psymon]

So I have the Knights Radiant chart as my wallpaper and I was looking at it this morning as my computer booted up, and I had a thought but am not good enough with computers to follow through with it. Has anyone tried to match up the chart with the Rose compass on the map of Roshar? It seems like the odd placement of the rose lines might match up with the center of the chart. Also do we know who the pictures are of that are on the border of that chart? I am kind of new to the site and haven't had the chance to research everything I want to yet.

[WeiryWriter]

Also do we know who the pictures are of that are on the border of that chart?

 

Those are depictions of the Heralds, although how much they actually look like the Heralds they are supposed to depict is unknown.

[Psymon]

Those are depictions of the Heralds, although how much they actually look like the Heralds they are supposed to depict is unknown.

That's what I thought, it's just that some of them look as though they might be female, and no I am not sexist, I just thought I remembered that they were all kings before they became Heralds, so I was just confused.

[WeiryWriter]

That's what I thought, it's just that some of them look as though they might be female, and no I am not sexist, I just thought I remembered that they were all kings before they became Heralds, so I was just confused.

 

Half of the Heralds were female, Jezrien is the only one who was said to be a King before being a herald.

[RShara]

That's what I thought, it's just that some of them look as though they might be female, and no I am not sexist, I just thought I remembered that they were all kings before they became Heralds, so I was just confused.

 

Half the Heralds are male, half are female.

 

Q:  Can you confirm the real names of the Heralds for me?

A:  Jezrien, Nale, Chanarach (nickname: Chana), Vedel, Paliah (nickname: Pali), Shalash (nickname: Ash), Battar, Kalak, Talenel (nickname: Taln), Ishar.

Jezrien-male

Nale-male

Chanarach-female

Vedel-female

Paliah-female

Shalash-female(Jezrien's daughter)

Battar-female

Kalak-male

Talenel-male

Ishar-male