On a class of fractal functions with graph Hausdorff dimension 2

T.F. Xie and S.P. Zhou

Chaos, Solitons & Fractals, 2007, vol. 32, issue 5, 1625-1630

Abstract: We prove that the graph of the continuous functiony=Φ(x)=∑k=1∞λ-kαϕλkβx,0⩽x⩽1has Hausdorff dimension 2, where λ>1, β>α>1, ϕ(x)=2x, 0⩽x⩽1/2, ϕ(−x)=ϕ(x) and ϕ(x+1)=ϕ(x).

Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:32:y:2007:i:5:p:1625-1630

DOI: 10.1016/j.chaos.2005.12.038

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