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Usage Examples

This document provides practical examples of using the Numerical Visualizations application.

Table of Contents

  1. Basic Usage
  2. Using the Toolbar
  3. Working with Presets
  4. Settings Dialog
  5. Exporting Images
  6. Programmatic Usage

Basic Usage

Selecting a Visualization

Via Keyboard Shortcuts:

Ctrl+1  → Newton's Method
Ctrl+2  → Mandelbrot Set
Ctrl+3  → Hailstone Sequence

Via Menu:

  1. Click Visualizations in the menu bar
  2. Click visualization name to use defaults
  3. Hover over name to see presets dropdown

First Time Launch

When you launch the app, you'll see:

┌────────────────────────────────────────┐
│                                        │
│  Select a visualization from the       │
│  Visualizations menu or press          │
│  Ctrl+1, Ctrl+2, or Ctrl+3            │
│                                        │
└────────────────────────────────────────┘

Just press Ctrl+1 to see Newton's Method with default settings!

Using the Toolbar

The toolbar provides instant display option toggling:

Example 1: Toggle Axes on Newton's Method

  1. Press Ctrl+1 (Newton's Method loads)
  2. Click [Axes] button in toolbar
  3. Axes appear instantly (~50ms) ⚡
  4. Click again to remove axes

Result: Coordinate reference overlay without recomputing the fractal!

Example 2: Customize Hailstone Display

  1. Press Ctrl+3 (Hailstone Sequence)
  2. Toolbar shows: [Axes] | [Point Labels] [Dots]
  3. Click [Point Labels] to hide (N, X, Y) labels
  4. Click [Dots] to hide endpoint markers
  5. Result: Just the colored path line

Button States:

  • Blue background = Enabled
  • Gray background = Disabled
  • Grayed out text = Not applicable (e.g., Point Labels on Newton)

Working with Presets

Example 1: Quick Exploration of Newton's Method

Goal: See different color schemes and detail levels

1. Click Visualizations → Newton's Method (hover)
2. Click "Default" → See balanced view
3. Click Visualizations → Newton's Method → "Vibrant Colors"
   → See bold color scheme
4. Click Visualizations → Newton's Method → "High Detail"
   → See 5000 iterations with ultra-precision

Example 2: Analyzing Hailstone Behavior

Goal: Study sequence at different time scales

1. Select Visualizations → Hailstone Sequence → "First 50 Steps - Early Behavior"
   → Zoomed view (ScaleFactor=0.08) of first 50 steps
   → Shows initial dynamics clearly

2. Switch to "300 Steps - Long Term Behavior"
   → Wider view (ScaleFactor=0.03) showing 300 steps
   → Point labels disabled (too crowded)
   → See where the sequence wanders over time

3. Compare to "Default - Balanced View"
   → Middle ground: 150 steps at 0.05 scale
   → All same starting point (-0.5, 0.3)!

Key Insight: Presets change analytical perspective (iterations, zoom), not just aesthetics.

Settings Dialog

Example 1: Fine-Tune Newton's Method

  1. Select Newton's Method
  2. Hover over Newton's Method → Click Settings...
  3. PropertyGrid opens showing categories
  4. Change MaxIterations to 2000
  5. Click Apply → See updated rendering (dialog stays open!)
  6. Change HueSpread to 30
  7. Click Apply → See new color scheme
  8. Click Close when satisfied

Example 2: Detailed Hailstone Configuration

  1. Select Hailstone Sequence
  2. Go to Settings...
  3. Adjust MaxIterations to 200
  4. Adjust ScaleFactor to 0.06
  5. Click Apply after each change to see effect
  6. Use toolbar to quickly toggle ShowAxes without opening settings again!

Exporting Images

Example 1: Export Newton Fractal for Publication

Goal: High-quality image with full metadata for paper

1. Press Ctrl+1 (Newton's Method)
2. Load "High Detail" preset
3. Toggle Axes on (if needed for reference)
4. File → Export → Export as PNG...
5. Save: "Newton_HighDetail_2024.png"

Result: PNG with embedded metadata:

  • Algorithm parameters (MaxIterations: 5000, Tolerance: 1e-12)
  • Color mapping formula
  • Coordinate system info
  • Timestamp

Use: Open in paper → Right-click → Properties → Details to verify settings

Example 2: SVG Export for Scalable Graphics

Goal: Vector graphic that scales to any size

1. Press Ctrl+3 (Hailstone Sequence)
2. Load "Default - Balanced View"
3. File → Export → Export as SVG...
4. Save: "Hailstone_Vector.svg"

Result: XML file with:

  • Vector path (infinitely scalable)
  • Complete metadata in <desc> tags
  • All algorithm parameters
  • Color palette documentation

Use: Open in web browser → Zoom to 1000% → Still perfect!

Example 3: Quick Share via JPEG

Goal: Smallest file for email/social media

1. Render any visualization
2. File → Export → Export as JPEG...
3. Save with automatic timestamped name

Result:

  • File size: ~150 KB (vs 800 KB PNG)
  • Basic metadata preserved
  • Good quality for sharing

Example 4: Viewing Export Metadata

After exporting PNG:

# Method 1: Windows built-in
Right-click image → Properties → Details → Comments

# Method 2: PowerShell script
.\View-ImageMetadata.ps1 "Newton_Method_20241219.png"

# Method 3: For SVG, just open in text editor
notepad "Hailstone_Sequence.svg"

What you'll see:

Visualization: Newton's Method
Algorithm Parameters:
  MaxIterations: 1200
  Tolerance: 1.00E-10
  HueSpread: 17
Color Mapping:
  Palette: Spectrum360 (360-degree HSV)
  Method: Hue = (angle + iterations * 17) mod 360
Display Settings:
  ShowAxes: true

Example 5: Batch Export for Comparison

Goal: Export all presets of a visualization

1. Select visualization (e.g., Mandelbrot - Ctrl+2)
2. For each preset:
   a. Visualizations → Mandelbrot Set → [Preset Name]
   b. File → Export → PNG
   c. Use auto-generated filename
3. Result: Multiple timestamped files for comparison

Files created:

Mandelbrot_Set_20241219_140122.png  (Classic)
Mandelbrot_Set_20241219_140145.png  (Deep Zoom)
Mandelbrot_Set_20241219_140208.png  (Psychedelic)

Programmatic Usage

Example 1: Creating a Custom Configuration

using NumericalVisualizations.Visualizations;

// Create custom Newton configuration
var config = new NewtonConfig
{
    MaxIterations = 3000,
    Tolerance = 1e-12,
    HueSpread = 25,
    ShowAxes = true
};

// Create visualization with custom config
var viz = new NewtonVisualization(config);

// Render to bitmap
var bitmap = viz.Render(1920, 1080, 4.0, 4.0);
bitmap.Save("custom_newton.png");

Example 2: Adding Axes Overlay Programmatically

using NumericalVisualizations.Performance;

// Render base visualization
var viz = new NewtonVisualization();
var bitmap = viz.Render(1920, 1080, 4.0, 4.0);

// Add axes overlay (fast!)
RenderingHelpers.DrawAxesOnBitmap(bitmap, 4.0, 4.0);

bitmap.Save("newton_with_axes.png");

Tips & Tricks

Performance

  • Axes Toggle: Use toolbar for instant axes on/off (Newton/Mandelbrot)
  • Fast Preview Presets: Use "Fast Preview" presets for quick exploration
  • Settings Apply: Click Apply multiple times to iterate on parameters

Visual Clarity

  • Hailstone Labels: Toggle Point Labels off when viewing 300 steps (too crowded)
  • Axes: Enable axes to understand coordinate space
  • Color Schemes: Try different HueSpread or ColorMultiplier values

See Also