6.1 Mysore:Shannon entropy computed using temporal data are listed in table 9a. Mysore is experiencing the sprawl in all directions as entropy values are closer to the threshold value (log (8) = 0.9). Lower entropy values of 0.007 (NW), 0.008 (SW) during 70’s shows an aggregated growth as most of urbanization were concentrated at city centre. However, the region experienced dispersed growth in 90’s reaching higher values of 0.452 (NE), 0.441 (NW) in 2009 during post 2000’s. The entropy computed for the city (without buffer regions) shows the sprawl phenomenon at outskirts. However, entropy values are comparatively lower when buffer region is considered. Shannon's entropy values of recent time confirms of minimal fragmented dispersed urban growth in the city.  This also illustrates and establishes the influence of drivers of urbanization in various directions.

Table 9a:  Shannon Entropy for Mysore

NE NW SE SW
2009 0.452 0.441 0.346 0.305
1999 0.139 0.043 0.0711 0.050
1992 0.060 0.010 0.0292 0.007
1973 0.067 0.007 0.0265 0.008

6.2 Shimoga: Shannon entropy was calculated to understand the state of urbanization direction wise in the study region (either fragmented or clumped) and are given in Table 9b. The analysis show of sprawl in the North West, while significant growth was observed in North East, South East and South west but fragmented due to presence of cultivable land in these regions.

Table 9b: Results of Shannon’s entropy:Shimoga

NE NW SE SW
1992 0.23 0.24 0.18 0.25
1999 0.39 0.41 0.34 0.36
2005 0.4 0.45 0.38 0.43
2010 0.43 0.7 0.42 0.47
Reference value 1.079 (Log(12))

6.3 Hubli-Dharwad:Shannon entropy computed using temporal data are listed in Table 9c. Hubli-Dharwad is experiencing the sprawl in all directions as entropy values inching closer to the threshold value (for Hubli: log (12) = 1.07 For Dharwad: log(7) = 0.845). Lower entropy values of 0.02 (NW), 0.011 (SW) during late 80’s shows an aggregated growth as most of urbanization were concentrated at city center. However, the region experienced dispersed growth in 90’s reaching higher values of 0.36 (NE), 0.49 (SE) in 2010 during post 2000’s. The entropy computed for the city (without buffer regions) shows the sprawl phenomenon at outskirts. However, entropy values are comparatively lower when buffer region is considered. Shannon's entropy values of recent time confirms of minimal fragmented dispersed urban growth in the city. This also illustrates and establishes the influence of drivers of urbanization in various directions.

Table 9c:  Shannon Entropy Index

Hubli NE NW SE SW Dharwad NE NW SE SW
1989 0.027 0.02 0.055 0.011 1989 0.011 0.013 0.008 0.006
2000 0.029 0.053 0.102 0.042 2000 0.016 0.023 0.014 0.018
2005 0.146 0.09 0.21 0.059 2005 0.08 0.086 0.09 0.0745
2010 0.369 0.134 0.49 0.128 2010 0.168 0.164 0.213 0.216

6.4 Gulbarga:Shannon entropy computed using temporal data are listed in Table 9d. Mysore is experiencing the sprawl in all directions as entropy values are closer to the threshold value (log (10) = 1). Lower entropy values of 0.018 (SW), 0.023 (SE) during 70’s shows an aggregated growth. However, the region show a tendency of dispersed growth during post 2000 with higher entropy values 0.268 (NE), 0.212 (NW) in 2010. Shannon's entropy values of recent time indicate of minimal but fragmented/dispersed urban growth in the region.

Table 9d:  Shannon Entropy Index

NE NW SE SW
2010 0.268 0.212 0.193 0.141
2002 0.139 0.112 0.091 0.098
1992 0.086 0.065 0.046 0.055
1973 0.067 0.034 0.023 0.018

6.5 Raichur: The entropy is calculated considering 7 gradients in 4 directions and are listed in table 9e. The reference value is taken as Log (7) which is 0.77 and the computed Shannon’s entropy values closer to this, indicates of sprawl. Increasing entropy values from 1973 to 2010 shows the tendency of dispersed growth of built-up area in the city with respect to 4 directions as we move towards the outskirts and this phenomenon is most prominent in SE and SW directions.

Table 9e:  Shannon Entropy Index

NE NW SE SW
2010 0.135 0.146 0.168 0.194
2002 0.078 0.083 0.084 0.097
1992 0.023 0.026 0.026 0.027
1973 0.01 0.006 0.007 0.005

6.6 Bellary: The entropy is calculated considering 10 gradients in 4 directions and are listed in table 9f. The reference value is taken as Log (10) which is 1 and the computed Shannon’s entropy values are inching closer to the threshold value, indicating tendency of sprawl. Increasing entropy values from 1973 to 2010 shows the tendency of dispersedgrowth of built-up area in the city with respect to 4 directions as we move towards the outskirts and this phenomenon is most prominent in SE and NE directions.

Table 9f:  Shannon Entropy Index

NE NW SE SW
2010 0.37 0.32 0.389 0.33
2005 0.23 0.25 0.26 0.24
2001 0.1 0.09 0.12 0.14
1973 0.04 0.03 0.08 0.06

6.7 Belgaum:The threshold limit of Shannon’s Entropy is log11 (1.04139). The results indicated that though Belgaum considering the buffer region has effect of urban sprawl considering the values of 1980 and 2012, and the effect is gaining strength temporally considering the threshold value of 1.041

Table 9g: Shannon’s Entropy Analysis

NE NW SE SW
1989 0.005967 0.019111 0.003412 0.008811
2000 0.028393 0.054622 0.017126 0.033461
2006 0.079145 0.14097 0.108442 0.113038
2012 0.086431 0.165239 0.115427 0.137098