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author: niplav, created: 2020-11-20, modified: 2022-06-06, language: english, status: notes, importance: 4, confidence: highly likely

The Diamond-Square algorithm is a terrain-generation algorithm for two dimensions (producing a three-dimensional terrain). I generalize the algorithm to any positive number of dimensions, and analyze the resulting algorithm.

Generalizing the Diamond-Square Algorithm to n Dimensions

Libre de la metáfora y del mito labra un arduo cristal: el infinito mapa de Aquel que es todas Sus estrellas.

Jorge Luis Borges, “Spinoza”, 1964

Introduction

Description

Square

Diamond

Analysis

Results

One Dimension

Space generated by the algorithm in one dimension

Two Dimensions

Space generated by the algorithm in two dimensions

Three Dimensions

Space generated by the algorithm in three dimensions