3D Visualization of Euler's Helix

DescriptionBackgroundThis model visualizes the Euler’s helix in 3D time space. This is a 3D representation of Euler's formula where the complex exponential function is plotted in 3D space, creating a helical curve that visually represents the relationship between sine and cosine functions as rotations around a central axis. The sine and cosine waves are orthogonal 2D projections of this 3D helix. The images below are taken as the inspiration and reference for this project: Now, this model has two planes (Real (Re) and Imaginary (Im) axes with time). The Complex number ‘z’ rotating anticlockwise in a circle at a constant rate with time. 𝑧(𝑡)=𝐴𝑒^𝑖𝑤𝑡 can be treated as a signal with time as independent variable and call it a complex sinusoid. The two equations from each plane are as follows: 𝑥(𝑡) = 𝐴𝑐𝑜𝑠(𝑤𝑡+𝜃) 𝑦(𝑡) =𝐴𝑠𝑖𝑛(𝑤𝑡+𝜃)𝑧(𝑡) = 𝑦(𝑡) + 𝑖𝑥(𝑡)𝐴𝑒^𝑖(𝑤𝑡+ 𝜃) = 𝐴𝑐𝑜𝑠(𝑤𝑡+𝜃) + i𝐴𝑠𝑖𝑛(𝑤𝑡+𝜃)Where 𝑤 → 2𝜋𝐹Frequency → 𝐹 (𝐹=1/𝑇) Phase → 𝜃Amp