Frontier physics
Fractals in physics
Vary the spectral exponent and amplitude of a synthetic fractal surface, observe the effective roughness across scales, then compare with the log M–log R plot to estimate the fractal dimension.
Equipment
- “Spectral exponent” β slider
- “Amplitude” slider of the ripples
- Rotatable self-similar 3D terrain mesh
- log M vs log R plot whose slope gauges the fractal dimension
Procedure
Change the spectral exponent and inspect roughness
Raise the “Spectral exponent” β slider: short-wavelength ripples lose amplitude faster, so the surface looks smoother at fine detail. Drag the figure to rotate it and note that self-similarity holds only over a finite range of scales.
Estimate the fractal dimension on the plot
Move to the log M–log R figure: measure the slope of the straight segment inside the observation window to read off the mass dimension via . Change “Amplitude” and check that the slope — the power law — does not depend on the overall amplitude.
State the limits of the power law
For two different β values, predict which surface is rougher at small scales, then verify on the figure. Explain why the model “does not represent a specific sample”: real materials are fractal only over a band of scales between atomic and sample sizes.