Overview
Thermal Erosion models loose material sliding downhill when height differences exceed a talus angle.
SpecializedSource checked
Thermal Erosion
Smooths steep terrain by moving material from unstable slopes to lower neighbors.
Quick Facts
Compact metadata for implementation and discovery.
- Category
- Procedural Generation
- Difficulty
- Intermediate
- Family
- Terrain Erosion
- Tier
- Specialized
- Status
- Verified
- Review
- Source Checked
- Sources
- 1
- Formulas
- 1
- Relationships
- 2
- Code example
- Ready
- Visualization
- Ready
Core Concepts
talus angleheight differencedownhill transferiterative relaxation
Quick facts
Complexity
Runtime and memory behavior at a glance.
Best
O(cells)
Average
O(iterations * cells)
Worst
O(iterations * cells)
Space
O(cells)
When to Use
- Use when terrain slopes should look more naturally settled.
- Use when terrain smoothing is a central requirement.
When Not to Use
- Avoid when sharp cliffs must be preserved exactly.
- Avoid when the generator cannot enforce the playability, connectivity, or style constraints required.
What It Does
- Finds steep neighboring height differences
- Moves material downhill
- Repeats until slopes stabilize
Use Cases
- Terrain smoothing
- Talus slope generation
- Post-processing rugged heightmaps
Inputs
- Height field
- Talus threshold
- Erosion rate
Outputs
- Relaxed height field
Key Formulas (1)
Slope threshold
move material if height[current] − height[neighbor] > talusthreshold
move material if height[current] - height[neighbor] > talus_thresholdDetects slopes that are too steep to remain stable.
Pseudocode
- 1.For each cell, compare height with neighboring cells
- 2.If a height difference exceeds the talus threshold, move material to lower neighbors
- 3.Repeat for several iterations
- 4.Return the stabilized height field
Canonical Example
- Input
- cell height = 10, neighbor height = 4, threshold = 3
- Output
- material moves to neighbor
- Explanation
- The slope is reduced because the height difference is too steep.
Implementation Notes
- Use a separate delta buffer per iteration to avoid order-dependent updates.
- Expose seed, scale, and constraint parameters so outputs can be reproduced.
- Keep a tiny example with expected output beside the implementation.
Common Pitfalls
- Too many iterations can over-smooth distinctive terrain shapes.
- 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 & TrajectoryShow sharp peaks shedding material into smoother slopes.
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G
Step 1 of 4: For each cell, compare height with neighboring cells
generated-gridNotes
Thermal erosion is simpler than hydraulic erosion and often used as a smoothing pass.
Sources (1)
What each reference supports for this entry.
Texturing and Modeling: A Procedural Approach
BookProcedural terrain reference for erosion-style slope relaxation and height-field modification.
Explore Next
Good next jumps from the relationship graph, ranked for useful discovery.
Relationships
View full relationship pageAlternative toHydraulic Erosion
Thermal erosion moves material by slope stability, unlike water-driven hydraulic erosion.
Related Algorithms
Tags
Procedural GenerationTerrainErosionSimulation