Today we are painting a landscape using mathematics.
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This is the link to the real-time rendering code (that you can edit yourself live) for the painting: https://www.shadertoy.com/view/4ttSWf

Music by Bent Stamnes (https://twitter.com/gloom303).

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0:00 Intro
0:48 Basic Polynomial Surface (Noise)
4:12 Fractal Surface (FBM)
6:28 Key Lighting
9:15 Atmospheric Coloring
11:00 Composition and Cliffs
12:28 Light Direction
13:53 Sky
15:42 Fill Lighting
17:42 Grass
18:31 Tree Sculpting
23:53 A Story of Painting with Maths professionally
24:52 Tree Lighting and Coloring
29:48 Highlights
32:05 Color Touchups
34:48 Clouds
40:32 Conclusion

Related articles I wrote:
* Fractal Noise Summation, also known as FBM: https://iquilezles.org/www/articles/fbm/fbm.htm
* Raymarching terrains: https://iquilezles.org/www/articles/terrainmarching/terrainmarching.htm
* Rendering SDFs: https://iquilezles.org/www/articles/raymarchingdf/raymarchingdf.htm
* Derivatives of Noise: https://iquilezles.org/www/articles/morenoise/morenoise.htm
* SDF of an Ellipsoid: https://iquilezles.org/www/articles/ellipsoids/ellipsoids.htm
* SDF Gradient: https://iquilezles.org/www/articles/normalsSDF/normalsSDF.htm
* Soft Shadows: https://iquilezles.org/www/articles/rmshadows/rmshadows.htm