The MiniBrot Period & Bulb Explorer builds on the same core idea as the Advanced Mandelbrot Period Bulb Calculator, but with a narrower lens. Instead of emphasizing general bulb detection anywhere in the set, it reframes the calculator for clicking points, estimating attracting-cycle periods, and using that information to inspect and identify individual minibrots and their associated bulbs. The underlying mathematics and detection logic remain essentially the same, but the presentation shifts toward exploration and classification through comparison and analysis of specific structures rather than general-purpose probing.
Instead of treating the set as purely visual, the app encourages you to probe structure directly, especially the difference between points inside clear hyperbolic components and points near boundaries or decorations. As a result, it leans toward exploration and classification more than artistic rendering. It’s meant to be lightweight, honest, and useful for navigating the set.
Special note: The technical details that follow are based on information provided by the AI assistant used to develop this application.
Good for…
- Curious beginners who want more than “pretty pictures”.
- Anyone learning iteration and complex dynamics.
- Hobbyists mapping bulbs or minibrots by period.
- Explorers comparing hyperbolic regions vs. decorations.
Not meant for…
- Formal proofs or symbolic classification.
- Deep-zoom perturbation rendering (extreme zoom research).
- Automatic naming of components, wakes, or internal addresses.
How it works
The app is designed to answer a simple but subtle question: Given a point in the Mandelbrot plane, does it lie in a hyperbolic component, and if so, what is the period of the attracting cycle? It answers this by iterating the critical orbit of (starting at ). If an attracting cycle is detected, the app reports its period and a rough confidence indicator. If the orbit escapes, the point is outside the Mandelbrot set. If neither conclusion is reliable —common near the boundary—, the result is reported as inconclusive rather than forced.
- Rendering: The app draws the Mandelbrot set using escape-time iteration, with smoothing for nicer gradients.
- Period estimation: When you click, it examines the late part (“tail”) of the critical orbit to see if it repeats.
- Attracting check: It also estimates whether the cycle is attracting (a key signature of hyperbolic components).
- Honest outcomes: Near the boundary or on decorations, the best answer is often inconclusive.
How to use
- Pan: click and drag on the canvas.
- Zoom: mouse wheel zooms around the cursor, and keeps your target under the pointer.
- Pick & analyze: click a point to run period detection for that c.
- Jump to coordinates: enter Center X and Center Y, then press “Go”.
- Copy values: use “Copy picked (CSV)” for coordinates, or “Copy link” to share your current view.
Interpreting results
After clicking a point, the app returns one of three outcomes:
- Outside: The orbit escapes, so it’s not in the Mandelbrot set.
- Periodic (period N): An attracting cycle was detected, which is strong evidence you’re inside a hyperbolic component (bulb).
- Inconclusive: This is common at boundaries and decorations. For better results, try higher iterations or move slightly inward.
Tips
- For reliable periods, click well inside a bulb, not on its edge.
- When analysis is inconclusive, try more iterations or move slightly inward from the boundary.
- Use a high-contrast palette when scanning for thin filaments and fine structure.
- Share views using “Copy link” before experimenting, so you can always return.
Limitations
- Finite iteration limits: Boundaries can look wrong or ambiguous until you increase iterations.
- Numerical precision: Zoom depth is limited by double-precision floating-point arithmetic.
- Heuristic detection: Period estimation is numerical and works best well inside clear hyperbolic components.
- No combinatorial labeling: The app does not compute roots, wakes, internal addresses, or external rays.
- No guaranteed classification: “Inconclusive” is expected on non-hyperbolic features and many boundary points.
Notice: For a simpler, bulb-only detector without classification context, see the Mandelbrot Period-Bulb Calculator.