Fractal Terrain Generation Using Random Midpoint Displacement Algorithm

The random midpoint displacement method is a classic fractal terrain generation algorithm whose core concept involves creating natural topographic variations by recursively subdividing line segments and randomly perturbing midpoint elevations. This approach leverages the self-similarity principle of fractal geometry, enabling the simulation of complex terrain features through simple rules.

The algorithm implementation can be divided into four key phases: During initialization, height values for both endpoints of the starting segment are set, typically to 0 to establish a base plane In each iteration, the algorithm bisects every current segment and calculates the midpoint position A random height displacement is applied to the midpoint, with displacement magnitude decreasing as iterations progress The subdivision and displacement processes repeat until reaching the preset iteration count

The algorithm's distinctive advantage lies in generating visually natural terrain contours through straightforward recursive operations. Adjusting the displacement amplitude parameter controls terrain roughness - smaller displacements yield smoother hills while larger values create rugged mountains.

In MATLAB implementations, arrays are typically used to store elevation data, with iterations handled through loops or recursive functions. Critical implementation considerations include boundary condition management and random number generator configuration, which directly impact final terrain realism. Generated terrain data can be visualized using MATLAB's 3D plotting capabilities, often employing functions like surf() or mesh() for topographic display. Key MATLAB functions involved may include rand() for random displacement generation and interpolation techniques for smooth elevation transitions between segments.