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Hydraulic Erosion

Shapes terrain by simulating water carrying and depositing sediment.

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Quick Facts

Compact metadata for implementation and discovery.

Category: Procedural Generation
Difficulty: Advanced
Family: Terrain Erosion
Tier: Specialized
Status: Verified
Review: Source Checked
Sources: 2
Formulas: 1
Relationships: 3
Code example: Ready
Visualization: Ready

Overview

Hydraulic Erosion moves water over a height field, eroding steep areas and depositing sediment where flow slows or capacity drops.

Core Concepts

water flowsediment capacityheight fieldmaterial deposition

Quick facts

Complexity

Runtime and memory behavior at a glance.

Best

O(cells)

Average

O(steps * cells)

Worst

O(steps * cells)

Space

O(cells)

When to Use

Use when generated terrain needs river-like channels and natural wear.
Use when terrain realism is a central requirement.

When Not to Use

Avoid when fast stylized terrain generation is more important than erosion detail.
Avoid when the generator cannot enforce the playability, connectivity, or style constraints required.

What It Does

Moves water over terrain
Computes sediment capacity
Erodes or deposits material
Evaporates water over time

Use Cases

Terrain realism
River channel generation
Heightmap post-processing

Inputs

Height field
Rain or droplet settings
Erosion parameters

Outputs

Eroded height field

Key Formulas (1)

Sediment capacity

capacity = slope · water_amount · velocity · factor

capacity = slope * water_amount * velocity * factor

Estimates how much material moving water can carry.

Pseudocode

1.Add water to terrain
2.Move water downhill
3.Compute sediment capacity from slope and flow
4.Erode when sediment is below capacity
5.Deposit when sediment exceeds capacity
6.Evaporate water

Canonical Example

Input: heightmap has a steep slope, water flows downhill
Output: channel is carved along the slope
Explanation: Flowing water removes sediment where capacity is high.

Implementation Notes

Run erosion on a copy and blend the result so the effect can be controlled.
Expose seed, scale, and constraint parameters so outputs can be reproduced.
Keep a tiny example with expected output beside the implementation.

Common Pitfalls

Unbounded erosion can flatten or destroy useful terrain features.
Random-looking output can still contain repeated patterns, dead ends, or invalid regions.
Not defining boundary, empty, or degenerate inputs before implementation.

Interactive Mechanism Walkthrough

2D Grid Wavefront & Trajectory

Show water paths carving channels into a heightmap.

Step 1 of 6: Add water to terrain

generated-grid

Notes

Small parameter changes can dramatically affect terrain style.

Sources (2)

What each reference supports for this entry.

Texturing and Modeling: A Procedural Approach

Book

Procedural terrain reference for erosion-style height-field modification and terrain texturing.

Interactive Terrain Modeling Using Hydraulic Erosion

Paper

Reference for interactive hydraulic terrain erosion with water flow, sediment transport, and deposition.

Open source

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Alternative toThermal Erosion

Procedural Generation · Specialized

Hydraulic and thermal erosion are terrain-weathering simulations with different transport models.

Compare with this

Often paired withTectonic Plate Terrain Generation