Math Constants is a comprehensive library of fundamental mathematical values available as high-precision floats. Instead of manually typing 3.14159... or approximating complex values like the Golden Ratio, this node provides instant access to 25 essential constants ranging from standard geometry (Pi, Tau) to advanced calculus (Euler's E) and chaos theory (Feigenbaum constants).
Usage & Behavior
This is a pure data source node. It takes no inputs and outputs a single float. It is designed to be plugged into Math, Vector Math, or Expression nodes to drive formulas with maximum precision. Using this node ensures your procedural patterns (like spirals, rotations, or phyllotaxis arrangements) are mathematically perfect.
Key Features
- High Precision: Returns float values with maximum available accuracy.
- 25 Constants: Covers Geometry, Calculus, Number Theory, and Physics.
- Workflow Speed: Eliminates the need to memorize or Google specific numbers.
Deep Dive: The Universe in Numbers
Beyond the basics like Pi, this node includes exotic constants essential for advanced proceduralism.
While the Golden Ratio ($\phi$) is perfect for 2D spirals, the Plastic Constant (approx 1.3247) is the minimal Pisot number. It is famously used in architecture (Padovan sequence) and is considered the "Golden Ratio of 3D space," ideal for 3D voxel packing and subdivision.
These constants are universal ratios found in Chaos Theory. They describe the point where a system (like dripping water or population growth) splits from orderly behavior into chaos. Essential for simulating realistic turbulence or bifurcation diagrams.
Parameters
- PI / TWO_PI: Basic circle constants ($3.141...$).
- INV_PI: $1 / \pi$. Useful for normalization.
- DEG_TO_RAD / RAD_TO_DEG: Conversion factors ($0.0174...$ / $57.29...$).
- GOLDENRATIO_PHI: The Golden Mean ($\approx 1.618$). Perfect for natural spirals.
- SQRT2 / SQRT3: Diagonal of a square and cube.
- PLASTIC: The minimal Pisot number ($\approx 1.324$).
- EULER_E: Base of natural logarithms ($2.718...$). Used for exponential decay.
- LN2 / LN10: Natural log of 2 and 10.
- EULERGAMMA: Euler-Mascheroni constant ($\gamma$).
- FEIGENBAUM (ALPHA/DELTA): Chaos bifurcation ratios.
- APERYS: Apéry's constant ($\zeta(3)$).
- CATALANS: Catalan's constant ($G$).
- KHINCHIN / GAUSS / OMEGA: Various number theory constants.
Quick Recipes
Practical uses for constants.
Perfect Rotation
- Constant DEG_TO_RAD
- Math Node Multiply
- Input B Angle (e.g. 90)
Phyllotaxis (Leaf Arrangement)
- Constant GOLDENRATIO_PHI
- Formula Angle * Phi
Exponential Decay
- Constant EULER_E
- Math Node Power
- Exponent -Time