發(fā)布時(shí)間：2018-04-10 12:17

  本文選題：城市形態(tài) + 分形��； 參考：《地理科學(xué)進(jìn)展》2017年05期

【摘要】：城市形態(tài)的分形是城市發(fā)育到一定階段涌現(xiàn)出的有序格局和復(fù)雜結(jié)構(gòu),其基本特征是空間分布的無(wú)尺度性質(zhì)。當(dāng)研究者基于某個(gè)顯著性水平推斷城市分維存在時(shí),實(shí)際上就是基于相應(yīng)的置信度判斷分形特征。雖然分形城市研究已經(jīng)多年,但大量有關(guān)維數(shù)測(cè)算的基礎(chǔ)問(wèn)題依然懸而未決。本文根據(jù)分形幾何學(xué)的基本思想論證城市形態(tài)分維測(cè)算的若干問(wèn)題。分維測(cè)量的準(zhǔn)則是最佳覆蓋——不多不少、恰到好處的覆蓋。盒子覆蓋是最容易理解的測(cè)量方法。采用盒子覆蓋法測(cè)量城市形態(tài)分維時(shí),應(yīng)考慮三個(gè)標(biāo)準(zhǔn):一是快速逼近,二是簡(jiǎn)便操作,三是穩(wěn)定擬合。直觀估計(jì)分維的辦法是利用雙對(duì)數(shù)坐標(biāo)圖。由于城市形態(tài)不是嚴(yán)格意義的分形,而是類似于文獻(xiàn)中的"前分形",測(cè)量尺度與相應(yīng)測(cè)度的冪律關(guān)系通常僅在一定尺度范圍內(nèi)有效,從而形成所謂標(biāo)度區(qū)。本文圍繞城市形態(tài)的分維測(cè)量和分形判斷開(kāi)展一系列討論,包括尺度選取、標(biāo)度區(qū)識(shí)別和統(tǒng)計(jì)標(biāo)準(zhǔn)等問(wèn)題,對(duì)今后城市分形研究具有理論啟示和方法論的參考價(jià)值。
[Abstract]:The fractal of urban form is an orderly pattern and complex structure that emerges in a certain stage of urban development, and its basic characteristic is the scale-free nature of spatial distribution.When researchers infer the existence of urban fractal dimension based on a significant level, it is actually based on the corresponding confidence level to judge fractal features.Although fractal cities have been studied for many years, a large number of basic problems related to dimension calculation are still unresolved.Based on the basic idea of fractal geometry, this paper discusses some problems in calculating the fractal dimension of urban morphology.The criterion of fractal dimension measurement is the best coverage-no more, no less, just the right coverage.Box coverage is the most easily understood method of measurement.Three criteria should be considered when measuring fractal dimension of urban morphology by box covering method: one is fast approaching, the other is simple operation, and the third is stable fitting.The method of intuitionistic estimation of fractal dimension is to use the double logarithmic coordinate graph.Since urban morphology is not a strict fractal, but is similar to the "pre-fractal" in the literature, the power-law relationship between the measurement scale and the corresponding measure is usually only valid within a certain scale range, thus forming the so-called scale area.In this paper, a series of discussions on fractal dimension measurement and fractal judgment of urban morphology are carried out, including the selection of scale, the identification of scale areas and statistical standards, etc., which have theoretical enlightenment and reference value of methodology for the future study of urban fractal.
【作者單位】： 北京大學(xué)城市與環(huán)境學(xué)院;
【基金】：國(guó)家自然科學(xué)基金項(xiàng)目(41671167)~~
【分類號(hào)】：C912.81;O189

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2 周作領(lǐng);樂(lè)軍;;分形幾何和動(dòng)力系統(tǒng)中的一些問(wèn)題[J];工程數(shù)學(xué)學(xué)報(bào);2006年05期

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本文編號(hào)：1731162