Two Sets of Simple Formulae to Estimating Fractal Dimension of Irregular Boundaries

Table 7

The shape index values of major cities in Beijing-Tianjin-Hebei region in 2000, 2005, and 2010.

City	Shape index in 2000					Shape index in 2005					Shape index in 2010
	Triangle	Square	Hexagon	Circle	Hexagram	Triangle	Square	Hexagon	Circle	Hexagram	Triangle	Square	Hexagon	Circle	Hexagram
Baoding	0.0082	0.0063	0.0055	0.0049	0.0109	0.0098	0.0075	0.0065	0.0059	0.0130	0.0099	0.0076	0.0066	0.0060	0.0132
Beijing	0.0099	0.0076	0.0066	0.0060	0.0132	0.0071	0.0055	0.0047	0.0043	0.0094	0.0057	0.0044	0.0038	0.0034	0.0076
Cangzhou	0.0155	0.0119	0.0103	0.0094	0.0207	0.0137	0.0105	0.0091	0.0083	0.0182	0.0150	0.0115	0.0100	0.0090	0.0200
Chengde	0.0118	0.0091	0.0079	0.0071	0.0157	0.0114	0.0088	0.0076	0.0069	0.0152	0.0120	0.0092	0.0080	0.0073	0.0160
Handan	0.0139	0.0107	0.0093	0.0084	0.0186	0.0107	0.0082	0.0071	0.0064	0.0142	0.0107	0.0082	0.0071	0.0064	0.0142
Hengshui	0.0220	0.0169	0.0146	0.0133	0.0293	0.0359	0.0277	0.0239	0.0217	0.0479	0.0300	0.0231	0.0200	0.0181	0.0400
Langfang	0.0239	0.0184	0.0160	0.0145	0.0319	0.0242	0.0187	0.0162	0.0147	0.0323	0.0260	0.0200	0.0173	0.0157	0.0347
Qinhuangdao	0.0137	0.0105	0.0091	0.0083	0.0182	0.0163	0.0125	0.0108	0.0098	0.0217	0.0222	0.0171	0.0148	0.0134	0.0295
Shijiazhuang	0.0152	0.0117	0.0101	0.0092	0.0203	0.0128	0.0098	0.0085	0.0077	0.0170	0.0128	0.0098	0.0085	0.0077	0.0170
Tangshan	0.0086	0.0066	0.0057	0.0052	0.0114	0.0085	0.0065	0.0056	0.0051	0.0113	0.0092	0.0071	0.0062	0.0056	0.0123
Tianjin	0.0051	0.0039	0.0034	0.0031	0.0068	0.0056	0.0043	0.0037	0.0034	0.0075	0.0069	0.0053	0.0046	0.0041	0.0091
Xingtai	0.0162	0.0125	0.0108	0.0098	0.0216	0.0174	0.0134	0.0116	0.0105	0.0232	0.0185	0.0142	0.0123	0.0112	0.0246
Zhangjiakou	0.0340	0.0262	0.0227	0.0206	0.0454	0.0332	0.0256	0.0221	0.0201	0.0443	0.0303	0.0233	0.0202	0.0183	0.0404
Average	0.0152	0.0117	0.0102	0.0092	0.0203	0.0159	0.0122	0.0106	0.0096	0.0212	0.0161	0.0124	0.0107	0.0097	0.0214