Hidden Things in Map of Roshar?

[Aether he/him]

Also, that Wikipedia animation is apparently a Julia set in four dimensions (and not the time-is-the-fourth-dimension 4D I'm at least kinda sorta acquainted with.) So.... no idea if that's significant or not. (Shadesmar is the 4th dimension?)

That is acutally a pretty cool notion. Would that mean that the Cognitive and Spiritual Realms are to be considered different dimensions as well? And to each of this have something equivalent to the Physical Realms three dimensions?

[Maffu17 he/him]

@ Peter

 

That's so unfair! I was watching that Julia Set animation weeks ago! (April 12th according to google history to be precise!) Curse my eyes!

 

Can we get an explanation as to how the incorrectly placed numbers had an impact? Or was that a separate unrelated easter egg?

[Maffu17 he/him]

Okay on reflection, it was only 8 days ago, but I was googling Julia Sets for hours that night, combining with geological features, galaxies, patterns on shells and fossils, and all the time it was staring me in the face! I wish I could grow an extra leg so I could kick myself with more efficiency.

[Maffu17 he/him]

I'm still curious how the ever storm is going to affect the geography in the long run if they can't find a way to stop it.

 

We saw it in Dalinar's vision when he was atop a single stone pillar surrounding by emptiness. 

The way I see it, each time the storms collide they cause massive damage (Plateau's spinning in the sky) and leave behind nothing but broken rock, now imagine ten thousand collisions across the surface of Roshar and you have the landscape from the vision. At least in my assumptions.

Edited April 21, 2014 by Maffu17

[RShara she/her]

So it WAS fractals!  Whoooo!  My mind can finally put this to rest.  Awesome job you guys!

 

Now how does this affect the history of Roshar?  Or maybe he meant the making of Roshar in writing?

[Shaggai]

So it wasn't an eroded dragon curve after all. Well, at least it's been cleared up.

[Grayv he/him]

I was think more long term. Will the "dragon head" parts be pushed towards the middle of the continent effectively closing off areas like the purelake?

[Iarwainiel I she/her]

This video (

) says that fractals have another dimension in between 2 and 3.

 

This is seriously weird and really cool stuff!

 

Wish I'd known about this before attending the WoR signing ... My wingman for the event is an extreme math geek who stronly prefers sci-fi to fantasy for the hard science aspect. Can't wait to tell him about this; maybe I can convince him to read WoK after all!

[Shaggai]

I just realized - Roshar and Shadesmar are both, geographically, two-dimensional representations of a three-dimensional cross-section of a four-dimensional Julia set. Seriously, that's a lot of abstraction. What sort of Shard would design something like that?

[Veil she/her]

I just realized - Roshar and Shadesmar are both, geographically, two-dimensional representations of a three-dimensional cross-section of a four-dimensional Julia set. Seriously, that's a lot of abstraction. What sort of Shard would design something like that?

 

Clearly it was Honor trying to be faithful to Cultivation's "artistic interpretation" of Odium's trolling.

[Ryshadium she/her]

Wow!  Amazing.  (I literally have no idea what any of this means)

[RShara she/her]

I'm sad to say goodbye to the Roshar-Greatshell theory though.

[Shaggai]

Clearly it was Honor trying to be faithful to Cultivation's "artistic interpretation" of Odium's trolling.

Either that or Adonalsium's a real jerk.

[Ryshadium she/her]

Rshara, I still believe.

[Confused]

As the creator of the Roshar-Greatshell theory (Post 159 on page 8), I also still have hope. We'll just have to name her "Julia"...

[Delightful]

Would it be possible for someone to explain the Julia Set thing in simple English please? I don't understand how you get the shape of Roshar.

(But if I need to understand complex mathematics to get it, don't worry, I'll just stand back and appreciate the hard work of all you mathematical folk )

[Youngy he/him]

I may be able to help with this... (Finished my Maths major a few years ago)

But it will take some reading, a textbook and some time. So I'll give a tentative "maybe" Delightful.

Edited April 22, 2014 by Youngy

[Sabrina Stormshard she/her]

Frickin' A! Finally! Well done guys

[Delightful]

I may be able to help with this... (Finished my Maths major a few years ago)

But it will take some reading, a textbook and some time. 

 

Please don't waste that amount of time on it if you could be doing something more useful!. I'm just curious, its not a big deal or anything.

That being said, thank you for even considering it!

 

[Argent he/him]

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) = - 0.25

x₃ = f(x₂) = f(-0.75) = - 0.3086

...

[May 2, 2016] Edit: My numbers were off, I was using two different formulas to compute x. The final result was still qualitatively the same, but the numbers are now correct.

 

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:

 

Edited May 2, 2016 by Argent

[Shaggai]

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:

 

Thank you so much for this. Now I understand.

[RShara she/her]

As the creator of the Roshar-Greatshell theory (Post 159 on page 8), I also still have hope. We'll just have to name her "Julia"...

Hey, I thought of it at the same time, you just beat me to posting

 

I'm down for naming Roshar-Greatshell Julia!  Do you think she's riding on the back of four giant elephants too?

 

Should I update the first post with all of the Easter Eggs?  (And what are they all?)

Edited April 22, 2014 by RShara

[Ryshadium she/her]

I think we all decided on the RosharShell around the same point of delirium.

 

I still think that there are some fun bits in the maps that aren't *this* thing that are worth discussing. No idea if they're relevant to anything, but it's been an amazing discussion to be a part of.

[RShara she/her]

Did we decide that the stamp on a lot of the maps were the cymatic pattern for Stormseat?

 

And I think you're right about Roshar-Greatshell.  WORSHIP HER!

[Ryshadium she/her]

O, Julia, Great Shell of Wonder, moving Westward through the seas.  Your gemheart powers us all. 

 

Perhaps the Church of Julia could give Stick a run for its money. 

Edited April 22, 2014 by Ryshadium