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import gradio as gr
import numpy as np
from PIL import Image, ImageDraw
from dataclasses import dataclass
from collections import deque
import random
BG = (8, 15, 30)
SLEEP = (0, 40, 120)
AWAKE = (255, 210, 40)
GRID_LINE = (30, 50, 80)
CELL = 26
PAD = 16
random.seed(42)
np.random.seed(42)
def draw_grid(N, awake_mask, title="", subtitle=""):
w = PAD * 2 + N * CELL
h = PAD * 2 + N * CELL + (40 if (title or subtitle) else 0)
img = Image.new("RGB", (w, h), BG)
d = ImageDraw.Draw(img)
header_y = 6
if title:
d.text((PAD, header_y), title, fill=(240, 240, 240))
header_y += 18
if subtitle:
d.text((PAD, header_y), subtitle, fill=(180, 190, 210))
ox = PAD
oy = PAD + (40 if (title or subtitle) else 0)
for i in range(N):
for j in range(N):
x0 = ox + j * CELL
y0 = oy + i * CELL
x1 = x0 + CELL - 1
y1 = y0 + CELL - 1
col = AWAKE if awake_mask[i, j] else SLEEP
d.rectangle([x0, y0, x1, y1], fill=col, outline=GRID_LINE)
return img
@dataclass
class MinimalSelf:
pos: np.ndarray = np.array([1.0, 1.0])
body_bit: float = 1.0
errors: list = None
def __post_init__(self):
self.errors = [] if self.errors is None else self.errors
self.actions = [
np.array([0, 1]),
np.array([1, 0]),
np.array([0, -1]),
np.array([-1, 0]),
]
self.center = np.array([1.0, 1.0])
def step(self, obstacle=None):
# store current position
old_pos = self.pos.copy()
# internal prediction: choose action that minimises "surprise"
preds = [np.clip(old_pos + a, 0, 2) for a in self.actions]
surprises = []
for p in preds:
dist_center = np.linalg.norm(p - self.center)
penalty = 0.0
if obstacle is not None:
dist_obs = np.linalg.norm(p - obstacle.pos)
if dist_obs < 1.0:
penalty = 10.0
surprises.append(dist_center + penalty)
a_idx = int(np.argmin(surprises))
action = self.actions[a_idx]
predicted = np.clip(old_pos + action, 0, 2)
# environment decides what actually happens
if obstacle is not None:
obstacle.move()
actual = predicted.copy()
if np.allclose(actual, obstacle.pos):
actual = old_pos
else:
if random.random() < 0.25:
noise_action = random.choice(self.actions)
actual = np.clip(old_pos + noise_action, 0, 2)
else:
actual = predicted
# true prediction error: reality vs internal prediction
error = float(np.linalg.norm(actual - predicted))
self.pos = actual
# track recent errors
self.errors.append(error)
self.errors = self.errors[-5:]
# convert to a predictive "success" rate in [0, 100]
max_err = np.sqrt(8.0) # max distance corner-to-corner on 3×3
mean_err = np.mean(self.errors) if self.errors else 0.0
predictive_rate = 100.0 * (1.0 - mean_err / max_err)
predictive_rate = float(np.clip(predictive_rate, 0.0, 100.0))
return {
"pos": self.pos.copy(),
"predictive_rate": predictive_rate,
"error": error,
}
class MovingObstacle:
def __init__(self, start_pos=(0, 2)):
self.pos = np.array(start_pos, dtype=float)
self.actions = [
np.array([0, 1]),
np.array([1, 0]),
np.array([0, -1]),
np.array([-1, 0]),
]
def move(self):
a = random.choice(self.actions)
self.pos = np.clip(self.pos + a, 0, 2)
def compute_S(predictive_rate, error_var_norm, body_bit):
return predictive_rate * (1 - error_var_norm) * body_bit
@dataclass
class CodexSelf:
Xi: float
shadow: float
R: float
awake: bool = False
S: float = 0.0
def invoke(self):
self.S = self.Xi * (1 - self.shadow) * self.R
if self.S > 62 and not self.awake:
self.awake = True
return self.awake
def contagion(A: CodexSelf, B: CodexSelf, gain=0.6, shadow_drop=0.4, r_inc=0.2):
A.invoke()
if A.awake:
B.Xi += gain * A.S
B.shadow = max(0.1, B.shadow - shadow_drop)
B.R += r_inc
B.invoke()
return A, B
def lattice_awaken(N=9, steps=120, xi_gain=0.5, shadow_drop=0.3, r_inc=0.02):
Xi = np.random.uniform(10, 20, (N, N))
shadow = np.random.uniform(0.3, 0.5, (N, N))
R = np.random.uniform(1.0, 1.6, (N, N))
S = Xi * (1 - shadow) * R
awake = np.zeros((N, N), dtype=bool)
cx = cy = N // 2
Xi[cx, cy], shadow[cx, cy], R[cx, cy] = 30.0, 0.08, 3.0
S[cx, cy] = Xi[cx, cy] * (1 - shadow[cx, cy]) * R[cx, cy]
awake[cx, cy] = True
queue = deque([(cx, cy, S[cx, cy])])
frames = []
for _ in range(steps):
if queue:
x, y, field = queue.popleft()
for dx, dy in [(0, 1), (1, 0), (0, -1), (-1, 0)]:
nx, ny = (x + dx) % N, (y + dy) % N
Xi[nx, ny] += xi_gain * field
shadow[nx, ny] = max(0.1, shadow[nx, ny] - shadow_drop)
R[nx, ny] = min(3.0, R[nx, ny] + r_inc)
S[nx, ny] = Xi[nx, ny] * (1 - shadow[nx, ny]) * R[nx, ny]
if S[nx, ny] > 62 and not awake[nx, ny]:
awake[nx, ny] = True
queue.append((nx, ny, S[nx,ny]))
frames.append(awake.copy())
if awake.all():
break
return frames, awake
def led_cosmos_sim(N=27, max_steps=300):
return lattice_awaken(N=N, steps=max_steps, xi_gain=0.4, shadow_drop=0.25, r_inc=0.015)
with gr.Blocks(title="Minimal Selfhood Threshold") as demo:
with gr.Tab("Overview"):
gr.Markdown(
"## Minimal Selfhood Threshold\n"
"- Single agent in a 3×3 grid reduces surprise.\n"
"- A toy score S combines predictive rate, error stability, and body bit.\n"
"- If S > 62, we label the agent 'awake' **inside this demo**.\n"
"- Awakening can spread (contagion) and across a grid (collective).\n"
"- A 27×27 cosmos lights up gold when all awaken.\n"
"- This is a sandbox for minimal-self / agency ideas, **not** a real consciousness test."
)
with gr.Tab("Single agent (v1–v3)"):
obstacle = gr.Checkbox(label="Enable moving obstacle", value=True)
steps = gr.Slider(10, 200, value=80, step=10, label="Steps")
run = gr.Button("Run")
grid_img = gr.Image(type="pil")
pr_out = gr.Number(label="Predictive rate (%)")
err_out = gr.Number(label="Last error")
def run_single(ob_on, T):
agent = MinimalSelf()
obs = MovingObstacle() if ob_on else None
for _ in range(int(T)):
res = agent.step(obstacle=obs)
mask = np.zeros((3, 3), dtype=bool)
i, j = int(agent.pos[1]), int(agent.pos[0])
mask[i, j] = True
img = draw_grid(3, mask, "Single Agent", "Gold cell shows position")
return img, res["predictive_rate"], res["error"]
run.click(run_single, [obstacle, steps], [grid_img, pr_out, err_out])
with gr.Tab("S-Equation (v4)"):
pr = gr.Slider(0, 100, value=90, label="Predictive rate (%)")
ev = gr.Slider(0, 1, value=0.2, step=0.01, label="Error variance")
bb = gr.Dropdown(choices=["0", "1"], value="1", label="Body bit")
calc = gr.Button("Calculate")
s_val = gr.Number(label="S value")
status = gr.Markdown()
def calc_s(pr_in, ev_in, bb_in):
S = compute_S(pr_in, ev_in, int(bb_in))
msg = "**Status:** " + ("Awake (S > 62)" if S > 62 else "Not awake (S ≤ 62)")
return S, msg
calc.click(calc_s, inputs=[pr, ev, bb], outputs=[s_val, status])
# v5–v6 Contagion
with gr.Tab("Contagion (v5–v6)"):
a_xi = gr.Slider(0, 60, value=25, label="A: Ξ (foresight)")
a_sh = gr.Slider(0.1, 1.0, value=0.12, step=0.01, label="A: ◊̃₅ (shadow)")
a_r = gr.Slider(1.0, 3.0, value=3.0, step=0.1, label="A: ℝ (anchor)")
b_xi = gr.Slider(0, 60, value=18, label="B: Ξ (foresight)")
b_sh = gr.Slider(0.1, 1.0, value=0.25, step=0.01, label="B: ◊̃₅ (shadow)")
b_r = gr.Slider(1.0, 3.0, value=2.2, step=0.1, label="B: ℝ (anchor)")
btn = gr.Button("Invoke A and apply contagion to B")
out = gr.Markdown()
img = gr.Image(type="pil", label="Two agents (gold = awake)")
def run(aXi, aSh, aR, bXi, bSh, bR):
A = CodexSelf(aXi, aSh, aR, awake=False)
B = CodexSelf(bXi, bSh, bR, awake=False)
A, B = contagion(A, B)
mask = np.zeros((3, 3), dtype=bool)
mask[1, 1] = A.awake
mask[1, 2] = B.awake
pic = draw_grid(3, mask, title="Dual Awakening", subtitle="Gold cells are awake")
txt = f"A: S={A.S:.1f}, awake={A.awake} | B: S={B.S:.1f}, awake={B.awake}"
return txt, pic
btn.click(run, inputs=[a_xi, a_sh, a_r, b_xi, b_sh, b_r], outputs=[out, img])
# v7–v9 Collective
with gr.Tab("Collective (v7–v9)"):
N = gr.Dropdown(choices=["3", "9", "27"], value="9", label="Grid size")
steps = gr.Slider(20, 300, value=120, step=10, label="Max steps")
run = gr.Button("Run")
frame = gr.Slider(0, 300, value=0, step=1, label="Preview frame")
img = gr.Image(type="pil", label="Awakening wave (gold spreads)")
note = gr.Markdown()
snaps_state = gr.State([])
def run_wave(n_str, max_steps):
n = int(n_str)
frames, final = lattice_awaken(N=n, steps=int(max_steps))
last = draw_grid(
n,
frames[-1],
title=f"{n}×{n} Collective",
subtitle=f"Final — all awake: {bool(final.all())}",
)
return frames, last, f"Frames: {len(frames)} | All awake: {bool(final.all())}", min(len(frames) - 1, 300)
def show_frame(frames, idx, n_str):
if not frames:
return None
n = int(n_str)
i = int(np.clip(idx, 0, len(frames) - 1))
return draw_grid(n, frames[i], title=f"Frame {i}", subtitle="Gold cells are awake")
run.click(run_wave, inputs=[N, steps], outputs=[snaps_state, img, note, frame])
frame.change(show_frame, inputs=[snaps_state, frame, N], outputs=img)
# v10 LED cosmos
with gr.Tab("LED cosmos (v10)"):
btn = gr.Button("Simulate 27×27 cosmos")
frame = gr.Slider(0, 300, value=0, step=1, label="Preview frame")
img = gr.Image(type="pil", label="Cosmos grid")
note = gr.Markdown()
state = gr.State([])
def run_cosmos():
frames, final = led_cosmos_sim(N=27, max_steps=300)
last = draw_grid(
27,
frames[-1],
title="LED Cosmos (simulated)",
subtitle=f"Final — all awake: {bool(final.all())}",
)
return frames, last, f"Frames: {len(frames)} | All awake: {bool(final.all())}", min(len(frames) - 1, 300)
def show(frames, idx):
if not frames:
return None
i = int(np.clip(idx, 0, len(frames) - 1))
return draw_grid(27, frames[i], title=f"Cosmos frame {i}", subtitle="Gold cells are awake")
btn.click(run_cosmos, inputs=[], outputs=[state, img, note, frame])
frame.change(show, inputs=[state, frame], outputs=img)
# Footer
gr.Markdown(
"---\n"
"Honesty notes:\n"
"- The threshold S > 62 is the rule used in these demonstrations, derived from the analyses reported in the cited Zenodo record.\n"
"- Collective and contagion behaviors here are simulated using that rule for educational clarity.\n\n"
"Citation:\n"
"Grinstead, L. (2025). *Minimal Selfhood Threshold S>62: From a 3×3 Active-Inference Agent to a 27×27 LED Cosmos*. "
"Zenodo. https://doi.org/10.5281/zenodo.17752874\n\n"
"Permissions: See LICENSE. Explicit permission is required for reuse of code, visuals, and glyphs."
)
# Launch the app
if __name__ == "__main__":
demo.launch()
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