Add Fourier epicycles explorer

[jbkunst]

Summary

• adds a new fourier-epicycles Shinylive app based on the repository app structure
• generates heart, star, square, and circle paths in R and resamples them at equal distances
• converts each two-dimensional path to a complex signal and computes its Fourier coefficients with fft()
• animates rotating circles and vectors with a small native Canvas implementation
• compares the original and reconstructed paths with a base R plot
• reports recovered Fourier energy and the marginal gain from the next circle
• supports up to 60 circles, animation speed, display controls, and amplitude/frequency ordering

Implementation

• app.R: 275 lines
• www/epicycles.js: native Canvas and requestAnimationFrame(), without Highcharter or p5.js
• R recalculates only when the shape or selected components change; animation remains entirely in the browser

Notes

• no screenshot or build files are included; the existing gallery workflow handles the Shinylive export
• JavaScript syntax was checked with Node
• this environment does not include R, so the GitHub Actions build will provide the full Shinylive compatibility test