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feat(plotly): implement phase-diagram (#3051)
## Implementation: `phase-diagram` - plotly Implements the **plotly** version of `phase-diagram`. **File:** `plots/phase-diagram/implementations/plotly.py` **Parent Issue:** #3004 --- :robot: *[impl-generate workflow](https://github.com/MarkusNeusinger/pyplots/actions/runs/20617610863)* --------- Co-authored-by: github-actions[bot] <github-actions[bot]@users.noreply.github.com> Co-authored-by: github-actions[bot] <41898282+github-actions[bot]@users.noreply.github.com>
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‎plots/phase-diagram/implementations/plotly.py‎

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""" pyplots.ai
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phase-diagram: Phase Diagram (State Space Plot)
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Library: plotly 6.5.0 | Python 3.13.11
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Quality: 93/100 | Created: 2025-12-31
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"""
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import numpy as np
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import plotly.graph_objects as go
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# Data - Damped pendulum showing spiral convergence to equilibrium
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np.random.seed(42)
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# Parameters for damped harmonic oscillator: d²x/dt² + 2ζω₀(dx/dt) + ω₀²x = 0
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omega_0 = 2.0 # Natural frequency
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zeta = 0.15 # Damping ratio (underdamped: 0 < zeta < 1)
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# Time array
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t = np.linspace(0, 15, 1500)
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dt = t[1] - t[0]
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# Analytical solution for underdamped oscillator
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omega_d = omega_0 * np.sqrt(1 - zeta**2) # Damped frequency
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# Initial conditions: x(0) = 2.0, dx/dt(0) = 0
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x0 = 2.0
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v0 = 0.0
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# Solution: x(t) = A * exp(-ζω₀t) * cos(ωd*t - φ)
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A = np.sqrt(x0**2 + ((v0 + zeta * omega_0 * x0) / omega_d) ** 2)
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phi = np.arctan2((v0 + zeta * omega_0 * x0) / omega_d, x0)
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x = A * np.exp(-zeta * omega_0 * t) * np.cos(omega_d * t - phi)
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dx_dt = -zeta * omega_0 * A * np.exp(-zeta * omega_0 * t) * np.cos(omega_d * t - phi) - omega_d * A * np.exp(
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-zeta * omega_0 * t
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) * np.sin(omega_d * t - phi)
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# Second trajectory with different initial condition (for basin structure)
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x0_2 = -1.5
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v0_2 = 3.0
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A2 = np.sqrt(x0_2**2 + ((v0_2 + zeta * omega_0 * x0_2) / omega_d) ** 2)
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phi2 = np.arctan2((v0_2 + zeta * omega_0 * x0_2) / omega_d, x0_2)
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x2 = A2 * np.exp(-zeta * omega_0 * t) * np.cos(omega_d * t - phi2)
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dx_dt_2 = -zeta * omega_0 * A2 * np.exp(-zeta * omega_0 * t) * np.cos(omega_d * t - phi2) - omega_d * A2 * np.exp(
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-zeta * omega_0 * t
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) * np.sin(omega_d * t - phi2)
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# Create figure
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fig = go.Figure()
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# Main trajectory with color gradient for time evolution
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fig.add_trace(
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go.Scatter(
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x=x,
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y=dx_dt,
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mode="lines+markers",
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name="Trajectory 1 (x₀=2.0, v₀=0)",
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line=dict(color="#306998", width=3),
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marker=dict(size=4, color=t, colorscale="Blues", showscale=False),
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hovertemplate="x: %{x:.2f}<br>dx/dt: %{y:.2f}<extra></extra>",
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)
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)
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# Second trajectory
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fig.add_trace(
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go.Scatter(
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x=x2,
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y=dx_dt_2,
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mode="lines+markers",
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name="Trajectory 2 (x₀=-1.5, v₀=3.0)",
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line=dict(color="#FFD43B", width=3),
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marker=dict(size=4, color=t, colorscale="YlOrBr", showscale=False),
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hovertemplate="x: %{x:.2f}<br>dx/dt: %{y:.2f}<extra></extra>",
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)
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)
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# Mark the fixed point (equilibrium at origin)
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fig.add_trace(
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go.Scatter(
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x=[0],
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y=[0],
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mode="markers",
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name="Fixed Point (Stable)",
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marker=dict(size=18, color="#E53935", symbol="x", line=dict(width=3)),
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hovertemplate="Equilibrium<br>x=0, dx/dt=0<extra></extra>",
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)
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)
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# Mark initial conditions
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fig.add_trace(
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go.Scatter(
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x=[x[0], x2[0]],
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y=[dx_dt[0], dx_dt_2[0]],
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mode="markers",
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name="Initial Conditions",
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marker=dict(size=14, color="#4CAF50", symbol="circle"),
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hovertemplate="Initial: x=%{x:.2f}, dx/dt=%{y:.2f}<extra></extra>",
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)
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)
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# Add direction arrows using annotations
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arrow_indices = [200, 500, 900]
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for idx in arrow_indices:
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# Arrow for trajectory 1
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fig.add_annotation(
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x=x[idx],
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y=dx_dt[idx],
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ax=x[idx - 30],
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ay=dx_dt[idx - 30],
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xref="x",
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yref="y",
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axref="x",
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ayref="y",
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showarrow=True,
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arrowhead=2,
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arrowsize=2,
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arrowwidth=2,
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arrowcolor="#306998",
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)
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# Arrow for trajectory 2
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fig.add_annotation(
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x=x2[idx],
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y=dx_dt_2[idx],
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ax=x2[idx - 30],
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ay=dx_dt_2[idx - 30],
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xref="x",
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yref="y",
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axref="x",
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ayref="y",
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showarrow=True,
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arrowhead=2,
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arrowsize=2,
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arrowwidth=2,
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arrowcolor="#FFD43B",
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)
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# Update layout
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fig.update_layout(
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title=dict(
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text="Damped Harmonic Oscillator · phase-diagram · plotly · pyplots.ai",
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font=dict(size=28),
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x=0.5,
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xanchor="center",
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),
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xaxis=dict(
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title=dict(text="Position x", font=dict(size=22)),
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tickfont=dict(size=18),
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gridcolor="rgba(0,0,0,0.1)",
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gridwidth=1,
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zeroline=True,
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zerolinecolor="rgba(0,0,0,0.3)",
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zerolinewidth=2,
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),
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yaxis=dict(
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title=dict(text="Velocity dx/dt", font=dict(size=22)),
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tickfont=dict(size=18),
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gridcolor="rgba(0,0,0,0.1)",
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gridwidth=1,
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zeroline=True,
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zerolinecolor="rgba(0,0,0,0.3)",
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zerolinewidth=2,
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),
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legend=dict(
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font=dict(size=16),
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x=0.02,
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y=0.98,
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bgcolor="rgba(255,255,255,0.9)",
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bordercolor="rgba(0,0,0,0.2)",
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borderwidth=1,
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),
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template="plotly_white",
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plot_bgcolor="white",
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margin=dict(l=80, r=40, t=100, b=80),
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)
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# Save as PNG (4800x2700 px)
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fig.write_image("plot.png", width=1600, height=900, scale=3)
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# Save interactive HTML
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fig.write_html("plot.html", include_plotlyjs=True, full_html=True)

‎plots/phase-diagram/metadata/plotly.yaml‎

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library: plotly
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specification_id: phase-diagram
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created: '2025-12-31T11:06:07Z'
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updated: '2025-12-31T11:15:34Z'
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generated_by: claude-opus-4-5-20251101
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workflow_run: 20617610863
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issue: 3004
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python_version: 3.13.11
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library_version: 6.5.0
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preview_url: https://storage.googleapis.com/pyplots-images/plots/phase-diagram/plotly/plot.png
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preview_thumb: https://storage.googleapis.com/pyplots-images/plots/phase-diagram/plotly/plot_thumb.png
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preview_html: https://storage.googleapis.com/pyplots-images/plots/phase-diagram/plotly/plot.html
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quality_score: 93
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review:
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strengths:
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- Excellent physics example with analytically correct damped harmonic oscillator
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solution
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- Multiple trajectories clearly demonstrate basin of attraction structure
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- Direction arrows effectively show time evolution without cluttering the plot
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- Color scheme provides excellent contrast and is colorblind-accessible
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- Title format correctly follows spec requirements
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- Hover templates provide useful interactivity showing exact x and dx/dt values
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- Fixed point and initial conditions clearly marked with distinct symbols
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- Clean, well-organized code structure
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weaknesses:
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- Marker size on trajectory lines (size=4) could be slightly larger for better visibility
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at full resolution
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- Grid opacity (0.1) is very subtle; 0.2-0.3 would provide better reference without
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being distracting
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- Axis labels lack units (though dimensionless is acceptable for theoretical phase
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diagrams)
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- Does not fully leverage Plotly animation features that could show trajectory evolution
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over time

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