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Published October 26, 2025 | Version v1
Model Open

Data visualization architecture: 3D plotting

Authors/Creators

Description

Data visualization architecture: 3D plotting 


Architect: Travis Raymond-Charlie Stone 

Assistant AI: Perplexity 

 
 
python
import sympy as sp # Define symbols N = sp.Symbol('N') # Number of spectral points or positions (spectrum) v = sp.Symbol('v') # Scaling factor per position (value) # Define a list of units or positional factors u, ..., n_k u, n2, n3, nk = sp.symbols('u n2 n3 nk') # Define spatial dimensions x, y, z x, y, z = sp.symbols('x y z') # Define permutation power p^3 or p^6 p = sp.Symbol('p') # Construct product of units/positions (assuming a simplified product) units_product = u * n2 * n3 * nk # Define the dimension permutation term (power) dimension_perm = (x, y, z) # Build the full symbolic formula: # (N spectrum) * (v value) * (units product) * (dimensions)^(p^3 permutations) spectrum_expression = N * v * units_product * (x * y * z) ** (p ** 3) # Display steps and full expression print("Symbolic multidimensional spectrum distribution formula:") sp.pprint(spectrum_expression) # Example: substitute numerical values for demonstration subs_values = {N: 10, v: 1.5, u: 2, n2: 3, n3: 4, nk: 5, x: 1, y: 1, z: 1, p: 3} numeric_result = spectrum_expression.subs(subs_values) print("\nExample evaluation with substituted values:") print(numeric_result)

This snippet defines symbolic variables for the key parameters N,v,u…nk,x,y,z,pN,v,u…nk,x,y,z,p, builds the spectrum model by multiplying spectrum magnitude, scaling, units over positions, and dimensional permutations, and then prints the symbolic formula. An example substitution with sample numeric values is also shown for evaluation.

This code can be adjusted to add more units or dimensions, extend permutations, or compute derivatives and simplifications symbolically, enabling further analysis of the multidimensional spectral distribution model with permutations in Python using SymPy.

  1. https://alexandrugris.github.io/maths/2017/04/30/symbolic-maths-python.html
  2. https://www.southampton.ac.uk/~fangohr/teaching/python/book/html/12-symbolic-computation.html
  3. https://maths-with-python.readthedocs.io/en/latest/07-sympy.html
  4. https://www.youtube.com/watch?v=j9Ps76MFbOE
  5. https://laro.lanl.gov/view/pdfCoverPage?instCode=01LANL_INST&filePid=13158136100003761&download=true
  6. https://scipy-lectures.org/packages/sympy.html
  7. https://www.geeksforgeeks.org/artificial-intelligence/spectrum-analysis-in-python/
  8. https://www.sciencedirect.com/science/article/pii/S2213133722000373
  9. https://caam37830.github.io/book/05_graphs/spectral.html

https://www.perplexity.ai/search/if-n1-1-n2-1-razSKecHSEiGvEP70F5iwA#15

 

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