## ----------------------------------------------------------------------------- # Core function for dynamic 3D-to-2D projection and multi-mode wave superposition generate_dynamic_octahedron <- function(mode = "baseline", k = NULL, t = 0, rotate = TRUE) { # Golden ratio constant used for biological capsid configurations phi <- (1 + sqrt(5)) / 2 if (is.null(k)) { k <- switch(mode, "baseline" = 8.0, # Fine-tuned harmonic baseline state "fluorite" = 14.0, # X-ray crystal lattice (Bragg, 1914) "capsid" = 3.24 * phi, # Capsid resonance via Golden Ratio "universe" = 23.0) # High frequency holographic boundary interference } vertices <- matrix(c( 1, 0, 0, -1, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 1, 0, 0, -1 ), ncol = 3, byrow = TRUE) if(rotate) { cos_t <- cos(t * 0.5) sin_t <- sin(t * 0.5) cx <- vertices[, 1] * cos_t + vertices[, 3] * sin_t cy <- vertices[, 2] * cos_t - vertices[, 3] * sin_t } else { # Protected pure Euclidean projection (Euclid Elements Book XIII) cx <- vertices[, 1] cy <- vertices[, 2] } grid_size <- 200 raumzeit_grid <- expand.grid( X = seq(-2.5, 2.5, length.out = grid_size), Y = seq(-2.5, 2.5, length.out = grid_size) ) wellen_feld <- numeric(nrow(raumzeit_grid)) for(i in 1:length(cx)) { # r <- sqrt((raumzeit_grid$X - cx[i])^2 + (raumzeit_grid$Y - cy[i])^2) welle <- cos(k * r - t) / (sqrt(r) + 0.1) wellen_feld <- wellen_feld + welle } raumzeit_grid$Intensitaet <- wellen_feld^2 stopifnot(sum(raumzeit_grid$Intensitaet) > 0) return(raumzeit_grid) } ## ----fig.align='center', fig.width=6, fig.height=5, echo=FALSE---------------- library(ggplot2) # Define the 6 primary spatial vertex coordinates (3D) according to Euclid vertices_3d <- data.frame( X = c(1, -1, 0, 0, 0, 0), Y = c(0, 0, 1, -1, 0, 0), Z = c(0, 0, 0, 0, 1, -1) ) # Precisely map the edge connections of the regular octahedron edges <- data.frame( x = c(1, 1, 1, 1, -1, -1, -1, -1, 0, 0, 0, 0), y = c(0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 1, -1), z = c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), xend = c(0, 0, 0, 0, 0, 0, 0, 0, 1, 1, -1, -1), yend = c(1, -1, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0), zend = c(0, 0, 1, -1, 0, 0, 1, -1, 0, 0, 0, 0) ) # Compute the 3D-to-2D parallel projection to render a clean spatial oblique view project_3d <- function(x, y, z) { x_proj <- x + 0.4 * z y_proj <- y + 0.4 * z return(data.frame(x = x_proj, y = y_proj)) } p_vert <- project_3d(vertices_3d$X, vertices_3d$Y, vertices_3d$Z) p_edges_start <- project_3d(edges$x, edges$y, edges$z) p_edges_end <- project_3d(edges$xend, edges$yend, edges$zend) faces <- data.frame( x = c(p_vert$x[c(1,3,5)], p_vert$x[c(1,4,5)], p_vert$x[c(2,3,5)], p_vert$x[c(2,4,5)]), y = c(p_vert$y[c(1,3,5)], p_vert$y[c(1,4,5)], p_vert$y[c(2,3,5)], p_vert$y[c(2,4,5)]), group = rep(1:4, each = 3) ) ggplot() + geom_polygon(data = faces, aes(x = x, y = y, group = group), fill = "#8A2BE2", alpha = 0.25) + geom_segment(aes(x = p_edges_start$x, y = p_edges_start$y, xend = p_edges_end$x, yend = p_edges_end$y), color = "#FFA500", linewidth = 0.8) + geom_point(aes(x = p_vert$x, y = p_vert$y), color = "#FFFFFF", size = 4) + #Euklidisches 3D-Raumkreuz fuer Theaitetos :) labs(title = "Figure 1: Euclidean 3D Framework") + theme_minimal() + theme( plot.background = element_rect(fill = "#05050A", color = NA), panel.background = element_rect(fill = "#05050A", color = NA), plot.title = element_text(color = "#FFA500", family = "mono", size = 11, face = "bold", hjust = 0.5), panel.grid = element_blank(), axis.text = element_blank(), axis.title = element_blank(), plot.margin = margin(20, 20, 20, 20) ) ## ----fig.align='center', fig.width=10, fig.height=5, echo=FALSE--------------- # Re-defining the internal core architecture for the demonstration chunk generate_vignette_octahedron <- function(mode = "baseline", t = 0, rotate = TRUE) { phi <- (1 + sqrt(5)) / 2 k <- switch(mode, "baseline" = 8.0, "capsid" = 3.24 * phi) vertices <- matrix(c( 1, 0, 0, -1, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 1, 0, 0, -1 ), ncol = 3, byrow = TRUE) if(rotate) { cos_t <- cos(t * 0.5) sin_t <- sin(t * 0.5) cx <- vertices[, 1] * cos_t + vertices[, 3] * sin_t cy <- vertices[, 2] * cos_t - vertices[, 3] * sin_t } else { cx <- vertices[, 1] cy <- vertices[, 2] } grid_size <- 200 raumzeit_grid <- expand.grid( X = seq(-2.5, 2.5, length.out = grid_size), Y = seq(-2.5, 2.5, length.out = grid_size) ) wellen_feld <- numeric(nrow(raumzeit_grid)) for(i in 1:length(cx)) { # CRAN FIX: Perfectly clean mathematical syntax for Euclidean distance r <- sqrt((raumzeit_grid$X - cx[i])^2 + (raumzeit_grid$Y - cy[i])^2) welle <- cos(k * r - t) / (sqrt(r) + 0.1) wellen_feld <- wellen_feld + welle } return(wellen_feld^2) } # === CRAN FIX START === # Save the current graphical parameters of the user oldpar <- par(no.readonly = TRUE) # === CRAN FIX END === # Set up side-by-side plotting area with a deep black background par(mfrow = c(1, 2), mar = c(1, 1, 3, 1), bg = "#05050A") # 1. Generate and plot the static baseline matrix (Left Panel) intensitaet_static <- generate_vignette_octahedron(mode = "baseline", t = 0, rotate = FALSE) matrix_static <- matrix(intensitaet_static, nrow = 200) image(matrix_static, col = colorRampPalette(c("#05050A", "#4B0082", "#8A2BE2", "#DAA520", "#FFFFFF"))(256), axes = FALSE, main = "// FIELD LOG: Static Baseline", col.main = "#FFA500", cex.main = 0.8) # 2. Generate and plot the pulsing capsid resonance matrix (Right Panel) intensitaet_dynamic <- generate_vignette_octahedron(mode = "capsid", t = pi/4, rotate = TRUE) matrix_dynamic <- matrix(intensitaet_dynamic, nrow = 200) image(matrix_dynamic, col = colorRampPalette(c("#05050A", "#4B0082", "#8A2BE2", "#FF6347", "#FFA500", "#FFFFFF"))(256), axes = FALSE, main = "// FIELD LOG: Pulsing Symmetry", col.main = "#FFA500", cex.main = 0.8) # === CRAN FIX START === # Immediately restore the user's original graphical parameters par(oldpar) # === CRAN FIX END ===