Multifractal for geographical data
Motivation
Is there Multifractality?
Economic geography
Some stores/facilities, some range of the length
Theory of agglomeration
Data analysis
Examine each stores/facilities, does it have multifractality and where.
Check Coefficient of determination for any considerable range of r
For each range, compare the multifractal of categories that have multifractality in the range
Comparing to population should be nice
An category can have some isolated ranges each of which has multifractality
Dispersal or Cluster
Poisson model
MAR and Jacobs, two kinds of Externalities
Can we construct a model to explain multifractal?
Restriction can generate multifractal?
Then, what is the feasible restriction?
経済地理学入門，山本健兒p49，図2-14
Lay, Social Geography of the city, Harper & Row, New York, 1983
p51-52,
欧米・日本：大都市圏の都心部：事務所，小売店舗，工業地区，集合住宅地区，一戸建て住宅地区，非都市的土地利用(農業)
Multifractal & Urban systems (Previous studies)
Gravity model for population distribution
Power law distribution
About q
Which q corresponds to multifractality? is discussed.
Applepy (1996) uses q>=0
"Abnormal spectrum" should be excluded. Hu et al. (2012),
Chen & Wang (2013)
Well discussed points
Monofractal or Multiracial?, Self-similar or Self-affine? seems to be well-discussed
"D1 and D2 vary in places even though D0 is the same", is often mentioned in such papers.