fix Makefile and README.md for 2012/blakely

2012/blakely/README.md

@@ -1,28 +1,32 @@
 # Most GIFted expressions
 
-Philip Blakely  
-Cambridge, UK  
-<pmblakely@gmail.com>  
+    Philip Blakely  
+    Cambridge, UK  
+    <pmblakely@gmail.com>  
 
+# To build:
 
-## Judges' comments:
-### To build:
-
-    make blakely
+```sh
+make
+```
 
 ### To run:
 
-    ./blakely "RPN formula" resolution > output.gif
+```sh
+./blakely "RPN formula" resolution > output.gif
+```
 
 ### Try:
 
-    ./blakely "xx*yy*+" 64 > paraboloid.gif
+```sh
+./blakely "xx*yy*+" 64 > paraboloid.gif
 
-    ./blakely 9 32 > empty.gif
+./blakely 9 32 > empty.gif
 
-    time ./blakely 0 250 > flat.gif
+time ./blakely 0 250 > flat.gif
+```
 
-### Selected Judges Remarks:
+## Judges' comments:
 
 Several IOCCC themes (RPN calculator, animated GIF generator, ray tracing) in one package! Very impressive!
 
@@ -30,21 +34,22 @@ The checkerboard pattern in the output can be broken. Could you figure out how?
 
 Larger GIF files confuse some image viewers.
 
-
 ## Author's comments:
-Remarks
--------
+
+### Remarks
 
 This program renders a generic RPN expression in ray-traced animated GIF form.
 The expression in spatial variables x and y is specified on the command-line with the required resolution,
 and an animated GIF showing a fly-around of the resulting surface is output to stdout.
 
-Usage
------
+### Usage
 
 The program should be run as:
 
-    ./blakely xy* 32 > pic.gif
+```sh
+./blakely xy* 32 > pic.gif
+```
+
 where the first parameter is a RPN expression, and the second is the width of the required GIF, up to a maximum of 250.
 
 The expressions are written in Reverse Polish Notation with the following characters recognised:
@@ -65,42 +70,40 @@ The surface plotted corresponds to -1 <= x,y <= 1 and for best results, the gene
 
 If there is a division by zero, square-root of a negative number, or similar operation, then the results are undefined.
 
-Examples
---------
+### Examples
 
 For test-runs, use a resolution of 32. For simple expressions, the GIF generation should take only
 a few seconds with a modern processor and full optimization. Run-time scales as O(N^3) with resolution N,
 and more complex expressions take longer to compute. For example, increasing the resolution of ripple.gif
 to 250 took ~35 minutes to render on an i7 processor.
 
-    ./blakely xy* 32 > saddle.gif
+```sh
+./blakely xy* 32 > saddle.gif
 
-    ./blakely xx*yy*1++d5*ct/ 64 > ripple.gif
+./blakely xx*yy*1++d5*ct/ 64 > ripple.gif
+```
 
-Algorithm
----------
+### Algorithm
 
 A generic root-finding algorithm to find the point of intersection between a ray
 and the surface is done using a simple forward search from the eye.
 In order to make the rendering realistic, both the value of the expression, and its derivative with respect to x and y must be tracked.
 This is done using an obvious stack-based approach.
 
-Obfuscations
-------------
+### Obfuscations
 
 Much of the obfuscation is achieved through the use of single-letter variables and #defines.
 The characters output for the GIF format are generated in myriad and wonderful ways, making use
 of XOR, return values from putchar, and odd expressions.
 The layout is in the form of X Y Z.
 
-Limitations
------------
+### Limitations
+
 ASCII is assumed since many bytes for the GIF output are generated from characters given in the source code.
 On compilation a few warnings about parentheses come up when using gcc 4.6.3, and one about no return value from main() (who uses exit codes anyway?),
 but clang 3.1 emits no warnings.
 
-Questions
----------
+### Questions
 
 * Apart from their appearance when computing the RPN expression, sin and cos are not used.
   How do we then get the correct angles for rotation?
@@ -111,11 +114,10 @@ Questions
 
 (Note that the author may or may not be able to answer all of the above questions.)
 
---------------------------------------------------------------------------------
-<!--
+## Copyright:
+
 (c) Copyright 1984-2015, [Leo Broukhis, Simon Cooper, Landon Curt Noll][judges] - All rights reserved
 This work is licensed under a [Creative Commons Attribution-ShareAlike 3.0 Unported License][cc].
 
 [judges]: http://www.ioccc.org/judges.html
 [cc]: http://creativecommons.org/licenses/by-sa/3.0/
--->