boofun.visualization

Visualization module for Boolean function analysis.

This module provides comprehensive plotting and visualization tools for Boolean functions, including influence plots, Fourier spectrum visualization, and interactive analysis tools.

Functions

`plot_function_comparison`(functions[, ...])	Compare multiple Boolean functions side by side.
`plot_hypercube`(f[, figsize, save_path, show])	Plot Boolean function on a hypercube graph (n ≤ 5).
`plot_sensitivity_heatmap`(f[, figsize, ...])	Plot sensitivity at each input as a heatmap.

Classes

BooleanFunctionVisualizer(function[, backend])

Comprehensive visualization toolkit for Boolean functions.

class boofun.visualization.BooleanFunctionVisualizer(function: BooleanFunction, backend: str = 'matplotlib')[source]

Comprehensive visualization toolkit for Boolean functions.

Provides static and interactive plots for Boolean function analysis, including influences, Fourier spectra, truth tables, and more.

__init__(function: BooleanFunction, backend: str = 'matplotlib')[source]

Initialize visualizer.

Parameters:

function – Boolean function to visualize
backend – Plotting backend (“matplotlib”, “plotly”)

plot_influences(figsize: Tuple[int, int] = (10, 6), save_path: str | None = None, show: bool = True) → Any[source]

Plot variable influences.

Parameters:

figsize – Figure size for matplotlib
save_path – Path to save the plot
show – Whether to display the plot

Returns:

Figure object

plot_fourier_spectrum(max_degree: int | None = None, figsize: Tuple[int, int] = (12, 8), save_path: str | None = None, show: bool = True) → Any[source]

Plot Fourier spectrum grouped by degree.

Parameters:

max_degree – Maximum degree to plot (None for all)
figsize – Figure size for matplotlib
save_path – Path to save the plot
show – Whether to display the plot

Returns:

Figure object

plot_truth_table(figsize: Tuple[int, int] = (10, 8), save_path: str | None = None, show: bool = True) → Any[source]

Plot truth table as a heatmap.

Parameters:

figsize – Figure size for matplotlib
save_path – Path to save the plot
show – Whether to display the plot

Returns:

Figure object

plot_noise_stability_curve(rho_range: ndarray | None = None, figsize: Tuple[int, int] = (10, 6), save_path: str | None = None, show: bool = True) → Any[source]

Plot noise stability as a function of correlation ρ.

Parameters:

rho_range – Range of ρ values to plot
figsize – Figure size for matplotlib
save_path – Path to save the plot
show – Whether to display the plot

Returns:

Figure object

create_dashboard(save_path: str | None = None, show: bool = True) → Any[source]

Create comprehensive analysis dashboard.

Parameters:

save_path – Path to save the dashboard
show – Whether to display the dashboard

Returns:

Dashboard figure

boofun.visualization.plot_function_comparison(functions: Dict[str, BooleanFunction], metric: str = 'influences', backend: str = 'matplotlib', **kwargs) → Any[source]

Compare multiple Boolean functions side by side.

Parameters:

functions – Dictionary mapping names to BooleanFunction objects
metric – Metric to compare (“influences”, “fourier”, “noise_stability”)
backend – Plotting backend
**kwargs – Additional plotting arguments

Returns:

Comparison plot

boofun.visualization.plot_hypercube(f: BooleanFunction, figsize: Tuple[int, int] = (10, 10), save_path: str | None = None, show: bool = True) → Any[source]

Plot Boolean function on a hypercube graph (n ≤ 5).

Shows the hypercube with vertices colored by function output. Edges connect inputs differing in one bit.

Parameters:

f – Boolean function (n ≤ 5)
figsize – Figure size
save_path – Optional path to save
show – Whether to display

Returns:

Figure object

boofun.visualization.plot_sensitivity_heatmap(f: BooleanFunction, figsize: Tuple[int, int] = (10, 8), save_path: str | None = None, show: bool = True) → Any[source]

Plot sensitivity at each input as a heatmap.

Parameters:

f – Boolean function (n ≤ 8 recommended)
figsize – Figure size
save_path – Optional path to save
show – Whether to display

Returns:

Figure object

class boofun.visualization.GrowthVisualizer(backend: str = 'matplotlib')[source]

Specialized visualizer for asymptotic behavior of Boolean function families.

Features: - Plot properties vs n with theoretical overlays - Compare multiple families - Visualize convergence rates - Show phase transitions

__init__(backend: str = 'matplotlib')[source]

Initialize growth visualizer.

Parameters:: backend – “matplotlib” or “plotly”

plot_growth(tracker: GrowthTracker, marker_name: str, show_theory: bool = True, show_error: bool = True, log_x: bool = False, log_y: bool = False, figsize: Tuple[int, int] = (10, 6), title: str | None = None, ax=None, **kwargs)[source]

Plot a single tracked property vs n.

Parameters:

tracker – GrowthTracker with computed results
marker_name – Which marker to plot
show_theory – Show theoretical prediction
show_error – Show error bars/ribbon (if available)
log_x – Use log scale
log_y – Use log scale
figsize – Figure size
title – Custom title
ax – Matplotlib axes (optional)

Returns:

Figure/axes

plot_family_comparison(trackers: Dict[str, GrowthTracker], marker_name: str, show_theory: bool = True, log_x: bool = False, log_y: bool = False, figsize: Tuple[int, int] = (12, 6), title: str | None = None)[source]

Compare a property across multiple function families.

Parameters:

trackers – Dict mapping family names to GrowthTrackers
marker_name – Property to compare
show_theory – Show theoretical predictions
log_x – Use log scale
log_y – Use log scale
figsize – Figure size
title – Custom title

Returns:

Figure

plot_convergence_rate(tracker: GrowthTracker, marker_name: str, reference: str = 'sqrt_n', figsize: Tuple[int, int] = (10, 6))[source]

Plot ratio of computed value to theoretical reference.

Useful for seeing convergence rates and constant factors.

Parameters:

tracker – GrowthTracker with results
marker_name – Property to analyze
reference – Reference function (“sqrt_n”, “n”, “log_n”, “constant”)
figsize – Figure size

Returns:

Figure

plot_multi_property_growth(tracker: GrowthTracker, marker_names: List[str] | None = None, figsize: Tuple[int, int] = (14, 4))[source]

Plot multiple properties side by side.

Parameters:

tracker – GrowthTracker with results
marker_names – Which markers to plot (None = all)
figsize – Figure size (per subplot)

Returns:

Figure

class boofun.visualization.LTFVisualizer(backend: str = 'matplotlib')[source]

Specialized visualizations for Linear Threshold Functions.

__init__(backend: str = 'matplotlib')[source]

plot_weight_distribution(weights: ndarray, figsize: Tuple[int, int] = (10, 6), title: str | None = None)[source]

Plot weight distribution of an LTF.

Parameters:

weights – LTF weight vector
figsize – Figure size
title – Custom title

Returns:

Figure

plot_influence_vs_weight(f: BooleanFunction, figsize: Tuple[int, int] = (8, 8))[source]

Scatter plot comparing |weight| vs influence.

Parameters:

f – Boolean function (should be LTF)
figsize – Figure size

Returns:

Figure

class boofun.visualization.ComplexityVisualizer(backend: str = 'matplotlib')[source]

Visualize query complexity measures and their relationships.

__init__(backend: str = 'matplotlib')[source]

plot_complexity_relations(f: BooleanFunction, figsize: Tuple[int, int] = (12, 5))[source]

Plot relationships between different complexity measures.

Shows s(f), bs(f), deg(f), C(f) and their bounds.

Parameters:

f – Boolean function
figsize – Figure size

Returns:

Figure

boofun.visualization.quick_growth_plot(family_name: str, properties: List[str] = ['total_influence', 'noise_stability'], n_values: List[int] | None = None, **kwargs)[source]

Quick way to visualize asymptotic behavior of a built-in family.

Parameters:

family_name – “majority”, “parity”, “tribes”, “and”, “or”, “dictator”
properties – Which properties to track
n_values – List of n values (default: odd 3-15)

Returns:

Figure

class boofun.visualization.DecisionTreeNode(is_leaf: bool = False, value: int | None = None, variable: int | None = None, left: DecisionTreeNode | None = None, right: DecisionTreeNode | None = None, depth: int = 0)[source]

Node in a decision tree for a Boolean function.

Can be either: - Internal node: queries a variable, has left (0) and right (1) children - Leaf node: outputs a constant value (0 or 1)

__init__(is_leaf: bool = False, value: int | None = None, variable: int | None = None, left: DecisionTreeNode | None = None, right: DecisionTreeNode | None = None, depth: int = 0)[source]

Create a decision tree node.

Parameters:

is_leaf – True if this is a leaf node
value – Output value for leaf nodes (0 or 1)
variable – Variable index to query for internal nodes
left – Child for variable=0
right – Child for variable=1
depth – Depth of this node in the tree

evaluate(x: int) → int[source]: Evaluate the decision tree on input x.

boofun.visualization.build_optimal_decision_tree(f: BooleanFunction, available_vars: List[int] | None = None, inputs: List[int] | None = None, depth: int = 0, max_depth: int = 20) → DecisionTreeNode[source]

Build an optimal (or near-optimal) decision tree for f.

Uses a greedy algorithm based on influence to select variables.

Parameters:

f – BooleanFunction to build tree for
available_vars – Variables not yet queried (None = all)
inputs – Current set of inputs to distinguish (None = all)
depth – Current depth in the tree
max_depth – Maximum allowed depth

Returns:

Root of the decision tree

boofun.visualization.plot_decision_tree(f: BooleanFunction, tree: DecisionTreeNode | None = None, figsize: Tuple[int, int] = (12, 8), save_path: str | None = None, show: bool = True, node_size: int = 2000, font_size: int = 10) → Any[source]

Plot a decision tree for a Boolean function.

Parameters:

f – BooleanFunction (used to build tree if not provided)
tree – Pre-built decision tree (None to build optimal)
figsize – Figure size
save_path – Path to save the plot
show – Whether to display
node_size – Size of tree nodes
font_size – Font size for labels

Returns:

Figure object

boofun.visualization.decision_tree_to_dict(node: DecisionTreeNode) → Dict[str, Any][source]: Convert decision tree to dictionary for serialization.

class boofun.visualization.InteractiveFunctionExplorer(f: BooleanFunction)[source]

Interactive widget for exploring a single Boolean function.

Features: - View truth table - View Fourier coefficients - View influences - Noise stability curve

__init__(f: BooleanFunction)[source]

Create explorer for a Boolean function.

Parameters:: f – Boolean function to explore

display()[source]: Show the interactive widget.

class boofun.visualization.GrowthExplorer(family_func: Callable[[int], 'BooleanFunction'], name: str = 'Function', n_range: tuple = (1, 12))[source]

Interactive widget for exploring how functions grow with n.

Features: - Slider to change n - Real-time plots of properties - Compare with theoretical bounds

__init__(family_func: Callable[[int], 'BooleanFunction'], name: str = 'Function', n_range: tuple = (1, 12))[source]

Create growth explorer.

Parameters:

family_func – Function that takes n and returns BooleanFunction
name – Name of the function family
n_range – (min_n, max_n) range for slider

display()[source]: Show the interactive widget.

class boofun.visualization.PropertyDashboard(functions: Dict[str, 'BooleanFunction'])[source]

Dashboard comparing multiple functions side by side.

__init__(functions: Dict[str, 'BooleanFunction'])[source]

Create dashboard for multiple functions.

Parameters:: functions – Dict mapping names to BooleanFunction objects

display()[source]: Show the dashboard.

boofun.visualization.create_function_explorer(f: BooleanFunction) → InteractiveFunctionExplorer[source]

Convenience function to create and display a function explorer.

Parameters:: f – Boolean function to explore
Returns:: InteractiveFunctionExplorer instance

boofun.visualization.create_growth_explorer(family_func: Callable[[int], 'BooleanFunction'], name: str = 'Function', n_range: tuple = (1, 12)) → GrowthExplorer[source]

Convenience function to create and display a growth explorer.

Parameters:

family_func – Function that takes n and returns BooleanFunction
name – Name of the function family
n_range – (min_n, max_n) range

Returns:

GrowthExplorer instance

class boofun.visualization.GrowthAnimator(family: FunctionFamily)[source]

Create animations showing function properties as n grows.

Example

>>> animator = GrowthAnimator(MajorityFamily())
>>> animator.animate("total_influence", n_range=(3, 15, 2))
>>> animator.save("majority_growth.gif")

__init__(family: FunctionFamily)[source]

Initialize animator with a function family.

Parameters:: family – BooleanFamily to animate

animate(property_name: str, n_range: Tuple[int, int, int] = (3, 15, 2), figsize: Tuple[int, int] = (10, 6), interval: int = 500, property_func: Callable | None = None) → animation.FuncAnimation[source]

Create animation of property growth.

Parameters:

property_name – Name of property to animate
n_range – (start, stop, step) for n values
figsize – Figure size
interval – Milliseconds between frames
property_func – Custom function to compute property (default uses builtin)

Returns:

Matplotlib animation object

animate_influences(n_range: Tuple[int, int, int] = (3, 15, 2), figsize: Tuple[int, int] = (12, 6), interval: int = 700) → animation.FuncAnimation[source]

Animate influence distribution as n grows.

Shows bar chart of influences with bars growing/shrinking.

Parameters:

n_range – (start, stop, step) for n values
figsize – Figure size
interval – Milliseconds between frames

Returns:

Matplotlib animation object

save(filename: str, fps: int = 2, **kwargs)[source]

Save animation to file.

Parameters:

filename – Output filename (supports .gif, .mp4)
fps – Frames per second
**kwargs – Additional arguments to animation.save()

show()[source]: Display the animation.

boofun.visualization.animate_growth(family: FunctionFamily, property_name: str = 'total_influence', n_range: Tuple[int, int, int] = (3, 15, 2), **kwargs) → animation.FuncAnimation[source]

Convenience function to create a growth animation.

Parameters:

family – BooleanFamily to animate
property_name – Property to track
n_range – (start, stop, step) for n values
**kwargs – Additional arguments to GrowthAnimator.animate()

Returns:

Matplotlib animation object

boofun.visualization.animate_influences(family: FunctionFamily, n_range: Tuple[int, int, int] = (3, 15, 2), **kwargs) → animation.FuncAnimation[source]

Convenience function to animate influence distribution.

Parameters:

family – BooleanFamily to animate
n_range – (start, stop, step) for n values
**kwargs – Additional arguments

Returns:

Matplotlib animation object

boofun.visualization.animate_fourier_spectrum(family: FunctionFamily, n_range: Tuple[int, int, int] = (3, 9, 2), figsize: Tuple[int, int] = (12, 6), interval: int = 800) → animation.FuncAnimation[source]

Animate Fourier spectrum (spectral weight by degree) as n grows.

Parameters:

family – BooleanFamily to animate
n_range – (start, stop, step) for n values
figsize – Figure size
interval – Milliseconds between frames

Returns:

Matplotlib animation object

boofun.visualization.create_growth_animation(family: FunctionFamily, properties: List[str] = None, n_range: Tuple[int, int, int] = (3, 15, 2), figsize: Tuple[int, int] = (14, 8), interval: int = 600) → animation.FuncAnimation[source]

Create multi-panel animation showing multiple properties.

Parameters:

family – BooleanFamily to animate
properties – List of properties to show (default: influence, degree, variance)
n_range – (start, stop, step) for n values
figsize – Figure size
interval – Milliseconds between frames

Returns:

Matplotlib animation object

Modules

`animation`	Animation utilities for Boolean function visualization.
`decision_tree`	Decision tree visualization for Boolean functions.
`decision_tree_export`	Decision Tree Export Utilities.
`growth_plots`	Growth and asymptotic visualization for Boolean function families.
`interactive`	Interactive visualizations using Plotly.
`latex_export`	LaTeX/TikZ Export for Boolean Function Visualizations.
`widgets`	Interactive Jupyter widgets for Boolean function exploration.