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On the simulation of continuous in scale universal multifractals,part I: Spatially continuous processes
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Cascadeprocessesgenericallyleadtomultifractalfieldsandhavebeenusedforsimulatingturbulent systems–includingclouds,rain,temperature,passivescalarsandthewind–aswellasforsolidearth fields, suchasrockdensity,magnetizationandtopography.Inspiteoftheirimportance,most applicationsuseprimitivediscretescaleratioprocesses,whichsingularizescaleswhichareinteger powersofintegers.Realisticsimulationsarecontinuousinscale,butsufferfromstrong‘‘finitesize effects’’i.e.deviationsfrompurepowerlawscaling,whichcantakesurprisinglylargerangesofscaleto disappear.Inthistwopartseries,wequantifyandshowtheoriginoftheproblemandquantifyits magnitude(partI),whileinpartIIweshowhowtolargelyovercomeitandgivea Mathematica code for the correspondingsimulationsforcausalandacausalspace-timesimulations.
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