Fix for typos in chapter 13

13/README.md

@@ -60,7 +60,7 @@ for (int i = 0; i < octaves; i++) {
 * When you have more than 4 octaves, try changing the lacunarity value.
 * Also with >4 octaves, change the gain value and see what happens.
 
-Note how with each additional octave, the curve seems to get more detail. Also note the self-similarity while more octaves are added. If you zoom in on the curve, a smaller part looks about the same as the whole thing, and each section looks more or less the same as any other section. This is an important property of mathematical fractals, and we are simulating that property in our loop. We are not creating a *true* fractal, because we stop the summation after a few iterations, but theoretically speaking, we would get a true mathematical fractal if we allowed the loop to continue forever and add an infinite number of noise components. In computer graphics, we always have a limit to how small details we can resolve, for example when objects become smaller than a pixel, so there is no need to make infinite sums to create the appearance of a fractal. A lot of terms may be needed sometimes, but never an infinite number.
+Note how with each additional octave, the curve seems to get more detail. Also note the self-similarity while more octaves are added. If you zoom in on the curve, a smaller part looks about the same as the whole thing, and each section looks more or less the same as any other section. This is an important property of mathematical fractals, and we are simulating that property in our loop. We are not creating a *true* fractal, because we stop the summation after a few iterations, but theoretically speaking, we would get a true mathematical fractal if we allowed the loop to continue forever and add an infinite number of noise components. In computer graphics, we always have a limit to the smallest details we can resolve, for example when objects become smaller than a pixel, so there is no need to make infinite sums to create the appearance of a fractal. A lot of terms may be needed sometimes, but never an infinite number.
 
 The following code is an example of how fBm could be implemented in two dimensions to create a fractal-looking pattern:
 
@@ -70,7 +70,7 @@ The following code is an example of how fBm could be implemented in two dimensio
 * Modify the lacunarity of the fBm on line 47
 * Explore by changing the gain on line 48
 
-This technique is commonly used to construct procedural landscapes. The self-similarity of the fBm is perfect for mountains, because the erosion processes that create mountains work in a manner that yields this kind of self-similarity across a large range of scales. If you are interested in this, use you should definitly read [this great article by Inigo Quiles about advance noise](http://www.iquilezles.org/www/articles/morenoise/morenoise.htm).
+This technique is commonly used to construct procedural landscapes. The self-similarity of the fBm is perfect for mountains, because the erosion processes that create mountains work in a manner that yields this kind of self-similarity across a large range of scales. If you are interested in this use, you should definitely read [this great article by Inigo Quiles about advanced noise](http://www.iquilezles.org/www/articles/morenoise/morenoise.htm).
 
 ![Blackout - Dan Holdsworth (2010)](holdsworth.jpg)
 
@@ -108,4 +108,4 @@ A less extreme example of this technique is the following code where the wrap is
 
 <div class='codeAndCanvas' data='clouds.frag'></div>
 
-Warping the texture coordinates with noise in this manner can be very useful, a lot of fun, and fiendishly difficult to master. It's a powerful tool, but it takes quite a bit of experience to use it well. A useful tool for this is to displace the coordinates with the derivative (gradient) of the noise. [A famous article by Ken Perlin and Fabrice Neyret called "flow noise"](http://evasion.imag.fr/Publications/2001/PN01/) is based on this idea. Some modern implementations of Perlin noise include a variant that computes both the function and it's analytical gradient. If the "true" gradient is not available for a procedural function, you can always compute finite differences to approximate it, although this is less accurate and involves more work.
+Warping the texture coordinates with noise in this manner can be very useful, a lot of fun, and fiendishly difficult to master. It's a powerful tool, but it takes quite a bit of experience to use it well. A useful tool for this is to displace the coordinates with the derivative (gradient) of the noise. [A famous article by Ken Perlin and Fabrice Neyret called "flow noise"](http://evasion.imag.fr/Publications/2001/PN01/) is based on this idea. Some modern implementations of Perlin noise include a variant that computes both the function and its analytical gradient. If the "true" gradient is not available for a procedural function, you can always compute finite differences to approximate it, although this is less accurate and involves more work.