Fractal model of engineering surfaces.

Closed Fractal Interpolation Surfaces

Based on the construction of bivariate fractal interpolation surfaces, we introduce closed spherical fractal interpolation surfaces. The interpolation takes place in spherical coordinates and with the transformation to Cartesian coordinates a closed surface arises. We give conditions for this construction to be valid and state some useful relations about the Hausdorff and the Box counting dimen...

Design and Reconstruction of Fractal Surfaces

E. Tosan, E. Guérin and A. Baskurti LIGIM EA 1899 Computer Graphics, Image and Modeling Laboratory Claude Bernard University, Lyon, France Bât. 710 43, bd du 11 novembre 1918 69622 Villeurbanne Cedex Tel.: (33) 4.72.44.58.85 Fax : (33) 4.72.43.13.12 E-mail: [et eguerin abaskurt]@ligim.univ-lyon1.fr March 15, 2002 Abstract A method for the design and reconstruction of rough surfaces is introduce...

On the Imaging of Fractal Surfaces

Field emission properties of fractal surfaces

The density of emission current by a rough surface with fractal structure is analyzed. A possible experimental setup is modeled by an irregular emitting surface, iteratively generated by a fractional Brownian motion FBM algorithm with roughness or Hurst exponent H=0.3 and a far away plane representing the anode. The boundaries are held at a fixed potential difference and the Laplace’s equation,...

On the Fractal Dimension of Rough Surfaces

Most natural surfaces and surfaces of engineering interest, e.g., polished or sandblasted surfaces, are self-affine fractal over a wide range of length scales, with the fractal dimension Df 1⁄4 2:15 0:15. We give several examples illustrating this and a simple argument, based on surface fragility, for why the fractal dimension usually is \2.3. A kinetic model of sandblasting is presented, which...