00001 #include "MusimatChapter9.h" 00002 MusimatChapter9Section(C091704d) { 00003 Print("*** Voss's Method ***"); 00004 /***************************************************************************** 00005 00006 Voss's Method 00007 00008 Martin Gardner (1978) reported a fractal noise generator attributed to Voss. A 00009 set of random variables xk are summed on each sample n, and the result is output. The random vari- 00010 ables are updated at different rates. If , then the k th variable is assigned a new random 00011 number Us. The index k ranges from 0 to N - 1. So x0 is randomized every sample, x1 is randomized 00012 every other sample, x2 is randomized every fourth sample, and so on, until finally xN-1 is only 00013 randomized every samples. We can code this method as follows: 00014 *****************************************************************************/ 00015 para1(); // Step into this function to continue. 00016 } 00017 00018 Real VossFracRand( Integer n, RealList L ) { 00019 Real sum = 0.0; 00020 Integer N = Length( L ); 00021 For(Integer k = 0; k < N; k = k + 1) { 00022 If (Mod(n, Integer(Pow(2, k))) == 0) { 00023 L[k] = Random(-1.0, 1.0); 00024 } 00025 sum = sum + L[ k ]; 00026 } 00027 Return(sum); 00028 } 00029 00030 Static Void para1() { 00031 /***************************************************************************** 00032 The following creates and prints a list of 128 fractal noise samples over four octaves: 00033 *****************************************************************************/ 00034 00035 RealList L(Random(), Random(), Random(), Random()); 00036 RealList R; 00037 00038 For (Integer n = 0; n < 128; n = n + 1) { 00039 R[n] = VossFracRand(n, L); 00040 } 00041 00042 Print("*** Voss' Fractal Method ***"); 00043 Print(R); 00044 00045 /***************************************************************************** 00046 Figure 9.32 shows how this noise is constructed by this method. Each function changes at a rate 00047 twice as fast as the previous function, and the functions are summed. Random values in the rapidly 00048 changing functions have only local influence, whereas values in the slowly changing functions extend 00049 their influence over many samples of the summed result, giving the result a fractal characteristic. 00050 *****************************************************************************/ 00051 } 00052 00054 /* $Revision: 1.3 $ $Date: 2006/09/05 08:02:46 $ $Author: dgl $ $Name: $ $Id: C091704d.cpp,v 1.3 2006/09/05 08:02:46 dgl Exp $ */ 00055 // The Musimat Tutorial © 2006 Gareth Loy 00056 // Derived from Chapter 9 and Appendix B of "Musimathics Vol. 1" © 2006 Gareth Loy 00057 // and published exclusively by The MIT Press. 00058 // This program is released WITHOUT ANY WARRANTY; without even the implied 00059 // warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. 00060 // For information on usage and redistribution, and for a DISCLAIMER OF ALL 00061 // WARRANTIES, see the file, "LICENSE.txt," in this distribution. 00062 // "Musimathics" is available here: http://mitpress.mit.edu/catalog/item/default.asp?ttype=2&tid=10916 00063 // Gareth Loy's Musimathics website: http://www.musimathics.com/ 00064 // The Musimat website: http://www.musimat.com/ 00065 // This program is released under the terms of the GNU General Public License 00066 // available here: http://www.gnu.org/licenses/gpl.txt 00067
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