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# C:/Musimathics_local/Musimat/MusimatChapter9/C091704c.cpp File Reference

`#include "MusimatChapter9.h"`

Go to the source code of this file.

## Functions
| MusimatChapter9Section (C091704c)

## Function Documentation

MusimatChapter9Section | ( | C091704c |  | ) |

Definition at line 2 of file C091704c.cpp.

    00002                                  {
    00003 Print("*** Fractional Brownian Motion ***");
    00004 /*****************************************************************************
    00005
    00006 Fractional Brownian Motion
    00007
    00008 The preceding Brownian number generator produces a high degree
    00009 of local similarity because subsequent points are constrained to remain relatively close to previous
    00010 points. But because the random increment at each step is independent, Brownian motion typically only
    00011 shows self-similarity in a region of its spectrum, so its fractal quality degenerates with scaling.
    00012
    00013 Fractional Brownian motion (fBm) is like Brownian motion, but the increments are no longer
    00014 independent. Instead, just as low-frequency ocean waves extend their influence over many cycles
    00015 of higher-frequency waves, in fBm, local rapidly fluctuating values are influenced by broader,
    00016 slower-moving values extending proportionately over the entire spectrum. As fBm is magnified,
    00017 it retains its statistically self-similar shape, and so it is fractal regardless of magnification.
    00018
    00019 Think of it this way. If we had an ideal tape recorder that accurately recorded all frequencies,
    00020 and we gradually increased the speed of a tape recording of Brownian noise, the character of the
    00021 noise would change (from a relatively low-frequency “whoosh” to a higher-frequency “whish”).
    00022 But a recording of fBm noise will sound the same regardless of playback speed. All speeds sound
    00023 the same because both the signal and the spectrum are self-similar at all levels of scale. A number
    00024 of methods can be used to generate fBm noises.
    00025
    00026 *****************************************************************************/
    00027 }}