Quantum Shape Controls

⚠️ Parameters changed - render required

Texture Mode

Visual Settings

Parameters

Controls the overall size of the shape. Higher values create larger forms.
Determines oscillation speed. Higher values create more complex patterns.
Controls quantum superposition effects and wave interference.
Zoom in or out to see the full shape. 0.10x is the default size.

Mathematical Concepts

Euler's Identitytheorem
e^(iπ) + 1 = 0
Euler's Identity
Creates exponential spiral patterns with complex oscillations
Riemann Zeta Functiontheorem
ζ(s) = Σ(1/n^s)
Riemann Zeta Function
Generates fractal-like patterns with infinite series convergence
Gaussian Curvaturetheorem
K = det(II)/det(I)
Gaussian Curvature
Produces smooth curved surfaces with exponential decay
Klein Bottle Surfaceaxiom
x⁴ + y⁴ + z⁴ = 1
Klein Bottle Surface
Creates self-intersecting non-orientable surfaces
Quantum Superpositionpostulate
|ψ⟩ = α|0⟩ + β|1⟩
Quantum Superposition
Adds time-dependent quantum oscillations and wave interference
Möbius Transformationlemma
f(z) = (az+b)/(cz+d)
Möbius Transformation
Warps space with conformal mappings and inversions
Poincaré Disk Modelaxiom
ds² = 4|dz|²/(1-|z|²)²
Poincaré Disk Model
Models hyperbolic geometry with bounded infinity
Jordan Curve Theoremtheorem
γ: S¹ → ℝ²
Jordan Curve Theorem
Creates complex closed curves with multiple harmonics

Quantum Mathematical Shape Explorer

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Active: 3 conceptsMode: asciiPerformance: PreviewQuantum: 50%Zoom: 0.10x