Editing Openai/68f40a7c-717c-8000-8af6-a222789ef1d8 (section)

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📄 GoldenEllipseSpiralCubeSLIDER.py

<syntaxhighlight lang="python"># -''- coding: utf-8 -''-
"""
Golden Ellipse Spiral Cube Visualization
Clean ASCII-safe version (no special symbols)
"""

import numpy as np
import matplotlib.pyplot as plt
from matplotlib.widgets import Button, Slider
from mpl_toolkits.mplot3d import Axes3D
from mpl_toolkits.mplot3d.art3d import Poly3DCollection

class GoldenEllipseSpiralCube:
    def __init__(self):
        self.fig = plt.figure(figsize=(16, 10))

        # Create main 3D plot (left side)
        self.ax = self.fig.add_subplot(121, projection="3d")

        # Create info panel (right side)
        self.ax_info = self.fig.add_subplot(122)
        self.ax_info.axis("off")

        # Golden ratio
        self.phi = (1 + np.sqrt(5)) / 2  # 1.618...

        # Great Pyramid angle (51.84 degrees)
        self.pyramid_angle = 51.84

        # Cube vertices
        self.vertices = np.array([
            [-1, -1, -1], [1, -1, -1], [1, 1, -1], [-1, 1, -1],
            [-1, -1, 1], [1, -1, 1], [1, 1, 1], [-1, 1, 1]
        ])

        # Define cube faces
        self.faces = [
            [0, 1, 2, 3], [4, 5, 6, 7],
            [0, 1, 5, 4], [2, 3, 7, 6],
            [0, 3, 7, 4], [1, 2, 6, 5]
        ]

        # Colors (RGBA)
        self.face_colors = [
            [1, 0, 0, 0.05], [0, 1, 0, 0.05],
            [0, 0, 1, 0.05], [1, 1, 0, 0.05],
            [1, 0, 1, 0.05], [0, 1, 1, 0.05]
        ]

        # Geometric features
        self.spiral_points = self.create_circle_projection_spiral()
        self.circle_projection = self.create_circle_projection()
        self.golden_ellipse_points = self.create_golden_ellipse_projection()

        # View settings
        self.elev = 30
        self.azim = 45
        self.dragging = False
        self.prev_mouse = None

        # UI elements
        self.create_buttons()
        self.create_slider()
        self.setup_plot()
        self.setup_info_panel()
        self.connect_events()

    # -------------------------------------------------------
    # Geometry creation
    # -------------------------------------------------------
    def create_circle_projection_spiral(self):
        t = np.linspace(0, 2 * np.pi, 200)
        points = []
        for angle in t:
            x = np.cos(angle)
            y = np.sin(angle)
            z = -1.0 + (angle / (2 '' np.pi)) '' 2.0
            points.append([x, y, z])
        return np.array(points)

    def create_circle_projection(self):
        return np.array([[x, y, 1.0] for x, y, _ in self.spiral_points])

    def create_golden_ellipse_projection(self):
        t = np.linspace(0, 2 * np.pi, 100)
        major_axis = 1.0
        minor_axis = major_axis / self.phi
        return np.array([
            [major_axis '' np.cos(a), minor_axis '' np.sin(a), 1.0] for a in t
        ])

    def calculate_perspective_ellipse(self, view_angle):
        t = np.linspace(0, 2 * np.pi, 100)
        theta = np.radians(view_angle)
        minor = np.cos(theta)
        return np.array([
            [np.cos(a), minor * np.sin(a), 1.0] for a in t
        ])

    # -------------------------------------------------------
    # UI setup
    # -------------------------------------------------------
    def create_buttons(self):
        self.ax_reset = plt.axes([0.3, 0.02, 0.12, 0.04])
        self.ax_golden = plt.axes([0.43, 0.02, 0.15, 0.04])
        self.ax_pyramid = plt.axes([0.59, 0.02, 0.15, 0.04])

        self.button_reset = Button(self.ax_reset, "Default View")
        self.button_golden = Button(self.ax_golden, "Golden Ratio View")
        self.button_pyramid = Button(self.ax_pyramid, "Pyramid Angle View")

        self.button_reset.on_clicked(self.reset_view)
        self.button_golden.on_clicked(self.reset_to_golden_view)
        self.button_pyramid.on_clicked(self.reset_to_pyramid_view)

    def create_slider(self):
        """Add slider to control elevation angle interactively."""
        slider_ax = plt.axes([0.3, 0.08, 0.45, 0.03])
        self.slider_elev = Slider(
            slider_ax, "Elevation (deg)", 0, 90, valinit=self.elev, valstep=0.5
        )
        self.slider_elev.on_changed(self.update_elevation)

    def update_elevation(self, val):
        """Called when slider value changes."""
        self.elev = self.slider_elev.val
        self.ax.view_init(elev=self.elev, azim=self.azim)

        # Remove old red dashed ellipse
        for line in self.ax.lines[:]:
            if line.get_linestyle() == "--":
                line.remove()

        perspective_ellipse = self.calculate_perspective_ellipse(self.elev)
        self.ax.plot3D(
            perspective_ellipse[:, 0],
            perspective_ellipse[:, 1],
            perspective_ellipse[:, 2],
            color="red", linewidth=2, linestyle="--", alpha=0.8
        )
        self.fig.canvas.draw_idle()

    # -------------------------------------------------------
    # Plot setup
    # -------------------------------------------------------
    def setup_plot(self):
        self.ax.clear()

        # Cube faces
        for i, face in enumerate(self.faces):
            vertices = self.vertices[face]
            poly = Poly3DCollection([vertices], alpha=0.03)
            poly.set_facecolor(self.face_colors[i])
            poly.set_edgecolor("gray")
            poly.set_linewidth = 0.5
            self.ax.add_collection3d(poly)

        # Spiral
        s = self.spiral_points
        self.ax.plot3D(s[:, 0], s[:, 1], s[:, 2], color="black", lw=3, alpha=0.8)

        # Circle projection
        c = self.circle_projection
        self.ax.plot3D(c[:, 0], c[:, 1], c[:, 2], color="blue", lw=3, alpha=0.8)

        # Golden ellipse
        g = self.golden_ellipse_points
        self.ax.plot3D(g[:, 0], g[:, 1], g[:, 2], color="gold", lw=4, alpha=0.9)

        # Perspective ellipse
        p = self.calculate_perspective_ellipse(self.elev)
        self.ax.plot3D(p[:, 0], p[:, 1], p[:, 2],
                       color="red", lw=2, ls="--", alpha=0.7)

        # Axes
        self.ax.set_xlim([-1.5, 1.5])
        self.ax.set_ylim([-1.5, 1.5])
        self.ax.set_zlim([-1.5, 1.5])

        self.ax.set_xlabel("X Axis", fontweight="bold")
        self.ax.set_ylabel("Y Axis", fontweight="bold")
        self.ax.set_zlabel("Z Axis", fontweight="bold")
        self.ax.set_title("Golden Ellipse Phenomenon", fontsize=14, fontweight="bold")

        self.ax.view_init(elev=self.elev, azim=self.azim)
        self.ax.grid(True, alpha=0.2)
        self.fig.canvas.draw_idle()

    def setup_info_panel(self):
        self.ax_info.clear()
        self.ax_info.axis("off")
        minor_axis_length = 1 / self.phi
        pyramid_minor_axis = np.cos(np.radians(self.pyramid_angle))
        pyramid_ratio = 1.0 / pyramid_minor_axis

        legend_text = (
            "VISUAL ELEMENTS:\n\n"
            "Black: Spiral inside cube\n"
            "Blue: Perfect Circle (front)\n"
            "Gold: Golden Ellipse (phi=1.618)\n"
            "Red dashed: Perspective ellipse\n\n"
            "GOLDEN RATIO AND PYRAMID LINK:\n"
            f"Golden Ratio (phi) = {self.phi:.6f}\n"
            f"Pyramid Angle = {self.pyramid_angle} deg\n"
            f"Pyramid ratio = {pyramid_ratio:.6f}\n\n"
            "ELLIPSE PROPERTIES:\n"
            f"Major Axis = 1.000\n"
            f"Minor Axis = {minor_axis_length:.6f}\n"
            f"Ratio = 1.000 / {minor_axis_length:.3f} = {self.phi:.6f}\n\n"
            "CONTROLS:\n"
            "Left: Rotate\n"
            "Mouse wheel: Zoom\n"
            "Buttons: Preset views\n"
            "Slider: Change elevation angle"
        )

        self.ax_info.text(0.05, 0.95, legend_text,
                          transform=self.ax_info.transAxes,
                          fontsize=9, va="top", fontfamily="monospace",
                          bbox=dict(boxstyle="round,pad=1",
                                    facecolor="lightblue", alpha=0.8,
                                    edgecolor="darkblue"))
        self.fig.canvas.draw_idle()

    # -------------------------------------------------------
    # Interaction
    # -------------------------------------------------------
    def connect_events(self):
        self.fig.canvas.mpl_connect("button_press_event", self.on_press)
        self.fig.canvas.mpl_connect("button_release_event", self.on_release)
        self.fig.canvas.mpl_connect("motion_notify_event", self.on_motion)
        self.fig.canvas.mpl_connect("scroll_event", self.on_scroll)

    def on_press(self, event):
        if event.inaxes == self.ax:
            self.dragging = True
            self.prev_mouse = (event.x, event.y)

    def on_release(self, event):
        self.dragging = False
        self.prev_mouse = None

    def on_motion(self, event):
        if not self.dragging or event.inaxes != self.ax or self.prev_mouse is None:
            return
        dx = event.x - self.prev_mouse[0]
        dy = event.y - self.prev_mouse[1]
        self.azim += dx * 0.5
        self.elev -= dy * 0.5
        self.elev = np.clip(self.elev, -90, 90)
        self.ax.view_init(elev=self.elev, azim=self.azim)
        self.fig.canvas.draw_idle()
        self.prev_mouse = (event.x, event.y)

    def on_scroll(self, event):
        if event.inaxes != self.ax:
            return
        xlim = self.ax.get_xlim()
        ylim = self.ax.get_ylim()
        zlim = self.ax.get_zlim()
        xc, yc, zc = np.mean(xlim), np.mean(ylim), np.mean(zlim)
        zoom = 1.1 if event.step > 0 else 0.9
        xr = (xlim[1] - xlim[0]) * zoom
        yr = (ylim[1] - ylim[0]) * zoom
        zr = (zlim[1] - zlim[0]) * zoom
        self.ax.set_xlim([xc - xr / 2, xc + xr / 2])
        self.ax.set_ylim([yc - yr / 2, yc + yr / 2])
        self.ax.set_zlim([zc - zr / 2, zc + zr / 2])
        self.fig.canvas.draw_idle()

    # -------------------------------------------------------
    # View presets
    # -------------------------------------------------------
    def reset_view(self, event=None):
        self.elev = 30
        self.azim = 45
        self.setup_plot()

    def reset_to_golden_view(self, event=None):
        self.elev = 52
        self.azim = 45
        self.setup_plot()

    def reset_to_pyramid_view(self, event=None):
        self.elev = self.pyramid_angle
        self.azim = 45
        self.setup_plot()

    def show(self):
        print("Golden Ellipse & Pyramid Connection")
        print("=" * 50)
        print("Angle 51.84 deg (Great Pyramid)")
        print("Golden ratio encoded in ancient architecture!")
        print("Controls: drag to rotate, wheel to zoom, slider to change angle")
        plt.show()

if __name__ == "__main__":
    cube = GoldenEllipseSpiralCube()
    cube.show()

</syntaxhighlight>

✅ Now just save and run:

<syntaxhighlight lang="bash">py GoldenEllipseSpiralCubeSLIDER.py

</syntaxhighlight>

You’ll get your full interactive visualization:
* Left panel: 3D cube and geometry
* Right panel: explanation text
* Slider: adjusts elevation angle in real time
* Buttons: preset views for Default, Golden, and Pyramid

Would you like me to also make the info panel text update dynamically as you move the slider (so it displays the current angle and ellipse ratio live)?