Update app.py

app.py

@@ -1,29 +1,64 @@
 import gradio as gr
-import hashlib, random, math
+import hashlib, random, matplotlib.pyplot as plt
+
+# === Mutation Engine ===
+operators = ["\\sin", "\\cos", "\\exp", "\\log", "\\nabla", "\\int", "\\frac{\\partial}{\\partial t}"]
+variables = ["x", "y", "t", "\\xi_1", "dP", "d\\Psi", "dT"]
+
+def mutate_formula(base, epoch):
+    # Structural mutation rules
+    if epoch % 5 == 0:
+        base = f"\\int ({base}) \\, dx"
+    elif epoch % 7 == 0:
+        base = f"\\nabla \\cdot ({base})"
+    else:
+        new_term = random.choice(operators) + "(" + random.choice(variables) + ")"
+        base = base + " + " + new_term
+    return base
 
-# === Epoch Formula Generator ===
 def run_epochs(n=50):
-    results = []
+    formulas = []
+    base = "x^2 + 1"  # starting point
     for epoch in range(1, n+1):
-        coeff = random.randint(1,5)
-        offset = epoch
-        formula = f"\\Lambda(\\xi_1, dP, d\\Psi, dT) = dP \\cdot \\xi_1^{coeff} + \\sqrt{{d\\Psi + dT + {offset}}} + \\log(dT+{offset+1}) - \\sin(d\\Psi+\\xi_1)"
-        seal = hashlib.sha512(formula.encode()).hexdigest()
-        results.append({
-            "Epoch": epoch,
-            "Formula (LaTeX)": formula,
-            "Seal": seal
-        })
-    return results
-
-# === Gradio Integration ===
+        base = mutate_formula(base, epoch)
+        seal = hashlib.sha512(base.encode()).hexdigest()
+        complexity = base.count("\\") + base.count("+")
+        formulas.append(f"**Epoch {epoch}**\n\n$$ {base} $$\n\nImmortality Glyph: `{seal[:32]}...`")
+    return "\n\n---\n\n".join(formulas)
+
+# === Complexity Plot ===
+def plot_complexity(n=50):
+    base = "x^2 + 1"
+    complexities = []
+    epochs = list(range(1, n+1))
+    for epoch in epochs:
+        base = mutate_formula(base, epoch)
+        complexity = base.count("\\") + base.count("+")
+        complexities.append(complexity)
+    plt.figure(figsize=(8,5), facecolor="black")
+    plt.plot(epochs, complexities, color="cyan", marker="o", linestyle="--")
+    plt.title("Symbolic Complexity Growth Across Epochs", color="white")
+    plt.xlabel("Epoch"); plt.ylabel("Complexity Score")
+    plt.grid(alpha=0.3); plt.gca().set_facecolor("black")
+    return plt.gcf()
+
+# === Gradio App ===
 with gr.Blocks(theme=gr.themes.Monochrome()) as demo:
-    gr.Markdown("# 🔢 Live Epoch Run — Formula Evolution")
-    gr.Markdown("Watch 50 epochs unfold as formulas mutate into higher symbolic forms.")
+    gr.Markdown("# 🌌 Resonance Atlas — The Living Codex")
+    gr.Markdown("Watch formulas evolve into higher symbolic forms across epochs. Each scroll is sealed with an Immortality Glyph.")
+
+    with gr.Tab("Codex Scrolls"):
+        run_button = gr.Button("Run 50 Epochs")
+        output = gr.Markdown()
+        run_button.click(fn=run_epochs, inputs=None, outputs=output)
 
-    run_button = gr.Button("Run 50 Epochs")
-    output = gr.JSON(label="Epoch Results")
+    with gr.Tab("Complexity Timeline"):
+        plot_button = gr.Button("Show Complexity Growth")
+        plot_output = gr.Plot()
+        plot_button.click(fn=plot_complexity, inputs=None, outputs=plot_output)
 
-    run_button.click(fn=run_epochs, inputs=None, outputs=output)
+    with gr.Tab("Immersion Mode"):
+        gr.Markdown("### Full‑screen dynamic visualization coming soon…")
+        gr.Markdown("Formulas pulse, glyphs glow, epochs unfold.")
 
 demo.launch()