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Quantum Shape Controls
✨ RENDER SHAPE ✨
⚠️ Parameters changed - render required
Texture Mode
Ascii
Dots
Blocks
Gradient
Matrix
Visual Settings
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Global Color
Parameters
Amplitude: 4.00
Controls the overall size of the shape. Higher values create larger forms.
Frequency: 1.00
Determines oscillation speed. Higher values create more complex patterns.
Quantum Coefficient: 0.50
Controls quantum superposition effects and wave interference.
Rotation Speed: 1.00
Zoom: 0.10x
Zoom in or out to see the full shape. 0.10x is the default size.
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Mathematical Concepts
Euler's Identity
theorem
e^(iπ) + 1 = 0
Color:
Euler's Identity
Creates exponential spiral patterns with complex oscillations
Riemann Zeta Function
theorem
ζ(s) = Σ(1/n^s)
Color:
Riemann Zeta Function
Generates fractal-like patterns with infinite series convergence
Gaussian Curvature
theorem
K = det(II)/det(I)
Color:
Gaussian Curvature
Produces smooth curved surfaces with exponential decay
Klein Bottle Surface
axiom
x⁴ + y⁴ + z⁴ = 1
Klein Bottle Surface
Creates self-intersecting non-orientable surfaces
Quantum Superposition
postulate
|ψ⟩ = α|0⟩ + β|1⟩
Quantum Superposition
Adds time-dependent quantum oscillations and wave interference
Möbius Transformation
lemma
f(z) = (az+b)/(cz+d)
Möbius Transformation
Warps space with conformal mappings and inversions
Poincaré Disk Model
axiom
ds² = 4|dz|²/(1-|z|²)²
Poincaré Disk Model
Models hyperbolic geometry with bounded infinity
Jordan Curve Theorem
theorem
γ: S¹ → ℝ²
Jordan Curve Theorem
Creates complex closed curves with multiple harmonics
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Quantum Mathematical Shape Explorer
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Active: 3 concepts
Mode:
ascii
Performance:
Preview
Quantum:
50%
Zoom:
0.10x