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Collatz Sequence
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NULLPHASE.NET
Collatz Map
Exploring smooth extensions of the 3n+1 dynamical system.
Viewpoint
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Preset
--- Custom ---
Standard Collatz (a=3)
Lyapunov Landscape
Period-Doubling Cascade
Chaos Window (a∈[1.12,1.68])
Critical Boundary (a≈1.68)
Golden Ratio (a=φ)
Feigenbaum (a≈δ=4.669)
27 --- The Rebel (111 steps)
97 --- Twin Peak (118 steps)
871 --- Long Haul (178 steps)
6171 --- The Summit (261 steps)
9663 --- Slow Burn (184 steps)
77031 --- The Holdout (350 steps)
The Skull (z₀=85)
The Geode (z₀=97)
The Cathedral (z₀=872)
The Archipelago (z₀=871)
The Jellyfish (z₀=213)
The Spiral (z₀=53)
The Fragmented (z₀=27)
The Labyrinth (z₀=880)
The Ciliate (z₀=77031)
z₀=2 (Power of 2)
z₀=4 (Square)
z₀=27 (The Rebel)
z₀=27 a-plane
z₀=97 a-plane
z₀=871 a-plane
Navigation
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Mode
z-Plane (Julia)
a-Plane (Parameter)
Buddhabrot (Experimental)
c-Plane (Additive)
θ-Plane (Phase)
Target z₀
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3n+1
Target a
Island
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Auto Zoom
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Samples
0
Dynamics
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Multiplier (a)
3.000
a₁
a∞
a꜀
3
δ
Iterations
200
Escape Radius
1e2
Conjugate (Ship)
Coloring
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Color Mode
Log2 (Classic)
General
Analytic (|a|)
None (Banded)
Distance Estimation
Period Detection
Parity Word
Degree Renormalization
Lyapunov Mapping
Palette
Ember
Gold Rush
Obsidian
Copper
Deep Space
Arctic
Twilight
Neon Noir
Synthwave
Forest
Toxic
Spectral
Inferno
Magma
Plasma
Viridis
Turbo
Cividis
Mako
Color Blending
OkLCH (Perceptual Hue)
Oklab (Perceptual Mix)
HSL
Linear RGB
Transfer
Log-Log [log(log(t))]
Logarithmic [log(t)]
Cube Root [t¹/³]
Square Root [t¹/²]
Linear [t]
Sine [sin(t)]
Sigmoid [S-curve]
Quantized [Stepped]
Smooth Banding [Cycles]
Power 1.5 [t¹·⁵]
Quadratic [t²]
Cubic [t³]
Quartic [t⁴]
Quintic [t⁵]
Exponential [eᵗ]
Strength
1.00
Density
1.0
Phase
0.500
Reverse Gradient
Cycle Palette
Off
Quality
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Anti-Aliasing
AA Adapt
2.00
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RE
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0.0000
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IM
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0.0000
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