About

Piet Mondrian's neoplastic compositions follow strict geometric rules: orthogonal black lines partition a plane into rectangles filled with primary colors (red #C0392B, blue #2471A3, yellow #F4D03F) and non-colors (white, grey, black). Replicating this by hand requires balancing asymmetry against visual weight - a rectangle's perceived mass scales with its area A multiplied by the color's saturation. This generator uses recursive binary space partitioning to subdivide a canvas, then applies Mondrian's empirical color distribution: approximately 55% white, 12% red, 12% blue, 10% yellow, 6% black, 5% grey. Line thickness defaults to 6px relative to a 800px canvas, matching the proportions in "Composition with Red, Blue, and Yellow" (1930). The tool approximates Mondrian's aesthetic heuristics. It does not model his later "Broadway Boogie Woogie" period, which abandoned thick black lines.

Formulas

The generator recursively subdivides a rectangle using binary space partitioning. At each recursion level d, the probability of splitting is:

P_split = P_base × decay^d

where P_base ≈ 0.95 and decay ≈ 0.85. Splitting stops when the cell dimension falls below a minimum size S_min. The split position t along the chosen axis is sampled uniformly from the range:

t ∈ [0.2 × L, 0.8 × L]

where L is the length of the axis being split. The axis choice is biased by aspect ratio: if w > h, vertical split probability increases proportionally to ww + h. Color assignment uses a weighted discrete distribution with cumulative probability thresholds.

The seeded PRNG uses the Mulberry32 algorithm:

s = s + 0x6D2B79F5

t = (s ⊕ (s >>> 15)) × (s | 1)

where s is the mutable state seeded from user input, and ⊕ denotes bitwise XOR. Output is normalized to [0, 1).

Reference Data

Painting	Year	Dominant Colors	Grid Complexity	Line Weight	Largest Rectangle %
Composition II in Red, Blue, and Yellow	1930	Red, Blue, Yellow, White	Low (9 cells)	Thick	~35%
Composition with Large Red Plane	1921	Red, Yellow, Blue, White, Grey	Medium (12 cells)	Medium	~40%
Tableau I	1921	Red, Blue, Yellow, Black, White	High (16 cells)	Thick	~25%
Composition No. III	1929	Red, Yellow, White	Low (7 cells)	Thick	~45%
Composition A	1923	Red, Blue, Yellow, Grey, White	Medium (14 cells)	Medium	~20%
Composition with Yellow, Blue, and Red	1937	Yellow, Blue, Red, White	Low (8 cells)	Thick	~50%
Composition No. 10	1939	White, Black lines only	High (20+ cells)	Thin-Medium	~15%
Broadway Boogie Woogie	1943	Yellow, Red, Blue, Grey	Very High (100+)	No black lines	~5%
Composition with Red	1936	Red, White	Low (6 cells)	Thick	~60%
Lozenge Composition	1925	Red, White, Yellow	Medium (10 cells)	Thick	~30%
Composition London	1940	Red, Blue, Yellow, White	Medium (13 cells)	Medium	~22%
Victory Boogie Woogie	1944	Yellow, Red, Blue, Grey	Very High	No black lines	~3%

Frequently Asked Questions

Mondrian spent weeks adjusting rectangle proportions by eye. This generator uses probabilistic subdivision which approximates but does not replicate his aesthetic judgment. Increasing the minimum cell size parameter reduces fragmentation and often produces more balanced results. Mondrian also avoided placing two large colored rectangles adjacent to each other - a constraint this algorithm does not enforce.

The seed initializes a Mulberry32 pseudorandom number generator. Identical seeds with identical parameters always produce the same composition. Changing the seed by even 1 produces a completely different layout. Seeds are stored in localStorage, so you can note a seed value and regenerate the same artwork later.

The canvas exports at its native pixel dimensions. For a standard A4 print at 300 DPI, set the canvas to at least 2480 × 3508 pixels. The generator supports canvas sizes up to 4096 × 4096 pixels. Line weight scales proportionally - a 6px line on an 800px canvas equals approximately 0.75% of canvas width.

Without aspect-ratio bias, a tall narrow rectangle could be split horizontally again, producing extremely thin strips that look nothing like Mondrian's work. Biasing toward splitting the longer dimension keeps cells closer to square, matching the proportions seen in Mondrian's canonical works from 1920-1940.

No. Broadway Boogie Woogie (1943) abandoned black grid lines entirely and used small colored segments along the grid lines themselves. This generator models Mondrian's earlier neoplastic period (approximately 1920-1940) which uses thick black orthogonal lines with filled primary-color rectangles. The Broadway style requires a fundamentally different algorithm based on line segmentation rather than area subdivision.