Some finitions

05_Mandelbulb/Mandelbulb.lhs

@@ -6,8 +6,11 @@ Some points:
    In particular the `mainLoop` function is a direct link to the C library (FFI).
    This function is clearly far from the functional paradigm.
    Could we make this better?
-   We will have two choices, or create our own `mainLoop` function to make it more functional.
-   Or deal with the imperative nature of the GLUT `mainLoop` function.
+   We will have two choices: 
+
+   - create our own `mainLoop` function to make it more functional.
+   - deal with the imperative nature of the GLUT `mainLoop` function.
+
    As one of the goal of this article is to understand how to deal with existing libraries and particularly the one coming from imperative languages, we will continue to use the `mainLoop` function.
 2. Our main problem come from user interaction.
    If you ask "the Internet", 
@@ -237,9 +240,9 @@ The rest is similar to the preceding sections.
 > ymandel :: Point -> Point -> Point -> Point
 > ymandel x y z = fromIntegral (mandel x y z 64) / 64
 
-I won't put how the magic occurs directly here.
-But all the magic occurs in the file `YGL.hs`.
-This file is commented a lot.
+I won't explain how the magic occurs here.
+If you are interested, just read the file [`YGL.hs`](code/05_Mandelbulb/YGL.hs).
+It is commented a lot.
 
 - [`YGL.hs`](code/05_Mandelbulb/YGL.hs), the 3D rendering framework
 - [`Mandel`](code/05_Mandelbulb/Mandel.hs), the mandel function

05_Mandelbulb/YGL.hs

@@ -1,6 +1,3 @@
--- The languages include needed because I wanted to use
--- (Point,Point,Point) instead of 
--- data Point3D = Point3D (Point,Point,Point) deriving ...
 {-
 The module YGL will contains most boilerplate
 And display details.
@@ -37,11 +34,20 @@ module YGL (
     -- The main loop function to call
     , yMainLoop) where
 
-import Numeric (readHex)
+-- A bunch of imports
+import Numeric (readHex) -- to read hexadecimal values
+
+-- Import of OpenGL and GLUT
+-- but, I use my own Color type, therefore I hide the definition
+-- of Color inside GLUT and OpenGL packages
 import Graphics.Rendering.OpenGL hiding (Color)
 import Graphics.UI.GLUT hiding (Color)
 import Data.IORef
+
+-- I use Map to deal with user interaction
 import qualified Data.Map as Map
+
+-- Some standard stuff
 import Control.Monad (when)
 import Data.Maybe (isNothing)
 
@@ -49,6 +55,7 @@ import Data.Maybe (isNothing)
 - Just take the time to follow me.
 --}
 
+
 -- | A 1D point
 type Point   = GLfloat 
 -- | A Scalar value

07_Conclusion/Conclusion.lhs

@@ -22,4 +22,4 @@ Such an optimization would have been harder by using directly the OpenGL library
 
 You should also want to make a more precise object. Because, the Mandelbulb is
 clearly not convex. But a precise rendering might be very long from 
-\\(O(n^2log n)\\) to \\(O(n^3)\\).
+O(n².log(n)) to O(n³).