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

Table 4

Two sets of fractal dimension estimation for boundary lines of major cities in Beijing-Tianjin-Hebei region in 2000.

City	Boundary dimension D(1)					Boundary dimension D(2)
	Triangle	Square	Hexagon	Circle	Hexagram	Triangle	Square	Hexagon	Circle	Hexagram
Baoding	1.8082	1.9917	2.2542	2.3389	2.3051	1.5901	1.6429	1.6734	1.6948	1.5359
Beijing	1.5603	1.6590	1.7790	1.8183	1.7524	1.4423	1.4794	1.5006	1.5154	1.4036
Cangzhou	1.7706	1.9690	2.2647	2.3634	2.3275	1.5480	1.6031	1.6351	1.6577	1.4915
Chengde	1.8440	2.0629	2.3969	2.5077	2.4960	1.5953	1.6533	1.6871	1.7108	1.5361
Handan	1.7183	1.8871	2.1254	2.2039	2.1505	1.5245	1.5751	1.6044	1.6249	1.4725
Hengshui	1.7204	1.9141	2.2039	2.3022	2.2541	1.5093	1.5638	1.5956	1.6179	1.4535
Langfang	1.6908	1.8747	2.1458	2.2380	2.1805	1.4910	1.5442	1.5751	1.5968	1.4367
Qinhuangdao	1.7618	1.9492	2.2225	2.3128	2.2715	1.5480	1.6015	1.6326	1.6543	1.4932
Shijiazhuang	1.6309	1.7671	1.9480	2.0077	1.9393	1.4739	1.5189	1.5448	1.5630	1.4274
Tangshan	1.7672	1.9356	2.1707	2.2465	2.2025	1.5666	1.6169	1.6460	1.6664	1.5147
Tianjin	1.6969	1.8222	1.9825	2.0333	1.9802	1.5403	1.5827	1.6070	1.6239	1.4963
Xingtai	1.7271	1.9071	2.1673	2.2539	2.2037	1.5241	1.5765	1.6069	1.6282	1.4703
Zhangjiakou	1.7012	1.9141	2.2497	2.3677	2.3237	1.4817	1.5390	1.5725	1.5961	1.4233
Average	1.7229	1.8964	2.1470	2.2303	2.1836	1.5258	1.5767	1.6062	1.6269	1.4735