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

Table 5

Two sets of fractal dimension estimation for boundary lines of major cities in Beijing-Tianjin-Hebei region in 2005.

City	Boundary dimension D(1)					Boundary dimension D(2)
	Triangle	Square	Hexagon	Circle	Hexagram	Triangle	Square	Hexagon	Circle	Hexagram
Baoding	1.7692	1.9440	2.1913	2.2716	2.2289	1.5634	1.6148	1.6446	1.6654	1.5105
Beijing	1.5750	1.6706	1.7856	1.8229	1.7614	1.4581	1.4943	1.5149	1.5293	1.4203
Cangzhou	1.7741	1.9672	2.2514	2.3455	2.3083	1.5544	1.6088	1.6403	1.6625	1.4988
Chengde	1.8523	2.0734	2.4117	2.5238	2.5150	1.6008	1.6591	1.6930	1.7168	1.5412
Handan	1.7553	1.9279	2.1719	2.2513	2.2057	1.5531	1.6043	1.6338	1.6545	1.5006
Hengshui	1.6349	1.8151	2.0825	2.1756	2.1033	1.4473	1.5001	1.5308	1.5524	1.3934
Langfang	1.6837	1.8648	2.1306	2.2209	2.1612	1.4870	1.5397	1.5704	1.5919	1.4330
Qinhuangdao	1.6972	1.8638	2.0991	2.1771	2.1192	1.5082	1.5585	1.5876	1.6080	1.4565
Shijiazhuang	1.6408	1.7746	1.9509	2.0086	1.9430	1.4844	1.5288	1.5544	1.5723	1.4384
Tangshan	1.7623	1.9283	2.1589	2.2332	2.1881	1.5642	1.6142	1.6430	1.6632	1.5127
Tianjin	1.6309	1.7380	1.8702	1.9124	1.8544	1.4977	1.5363	1.5584	1.5738	1.4575
Xingtai	1.7119	1.8885	2.1430	2.2279	2.1739	1.5136	1.5655	1.5956	1.6167	1.4603
Zhangjiakou	1.7018	1.9133	2.2453	2.3617	2.3171	1.4830	1.5402	1.5736	1.5970	1.4249
Average	1.7069	1.8746	2.1148	2.1948	2.1446	1.5166	1.5665	1.5954	1.6157	1.4652