The MandelScope Deep Zoomer is my next step after my first effort at building a fractal explorer. This time, I wanted to go deeper into the same set, so this one pushes magnification as far as JavaScript reasonably allows in a browser. The idea is to inspect subtle features that aren’t visible in MandelScope, such as fine boundary structure and tiny secondary formations.
A warning is necessary: Deep zooming requires far more numerical precision and computational power than a browser-based tool can provide, so this app is constrained by performance and floating-point limits. That means that it can become painfully slow and sluggish at extreme magnifications. These are fundamental trade-offs between browser accessibility and deep zoom precision.
This app can also serves as a diagnostic tool for testing whether “structures” users are seeing are stable or likely artifacts caused by low iterations, coloring choices, or limited numeric precision. By systematically adjusting parameters—be it iteration count, bailout radius, precision settings, and coloring logic—you can distinguish genuine mathematical features from visual artifacts. This helps verify whether observed structures represent real properties of the set or computational approximations.
Who is this for?
This tool is for users who want to go very deep into the Mandelbrot set while keeping results reproducible: researchers, hobbyists hunting spurious minibrots (sometimes called “ghost” or fake ones, one of the reasons for building it) and other boundary artifacts, and anyone who prefer controls that behave more like a lab instrument than a wallpaper generator. Yes, you won’t be creating impressive imagery with this one: it’s built for analysis and verification, not polished artworks.
Special note: The technical details that follow are based on information provided by the AI assistant used to develop this application.
What makes it different to MandelScope
- High precision option: Selectable BigInt fixed‑point mode (selectable 128, 192, 256 or320 bits) that avoids floating-point rounding errors at extreme magnifications. This keeps orbit calculations numerically stable when double precision can no longer represent meaningful coordinate differences.
- Diagnostic‑first coloring: Includes binary escape threshold detection and adjustable bailout radius with escape gamma control slider designed to stress-test potential “interior” points and distinguish genuine features from rendering artifacts.
- Reproducible exploration: Full state export (center coordinates, scale, iterations, precision mode, palette, shift, gamma, bailout, threshold) allows you to recreate and share your discoveries with accuracy.
- Deliberate exclusions: Omits histogram‑normalized coloring and contrast stretching iteration coloring because it can make artifacts look convincingly real, in case you’re looking for elusive features.
Key features
- Deep zoom engine: Toggle high precision mode, choose precision levels, and keep zoom center stable via Zoom + / Zoom − buttons.
- View controls: Numeric center coordinates (Re(c), Im(c)), numeric scale (complex units per pixel), and zoom depth readout.
- Iterations: Adjustable up to 200,000 with quick +/− buttons (and a “Keeping fine detail” hint). Note that even very high iteration counts don’t guarantee accuracy at extreme zooms if numeric precision is insufficient. Therefore, iteration depth and precision must be increased together.
- Color modes: Smooth escape, Escape‑time, Interior solid, and Binary (threshold). The last one in particular is valuable for discarding smooth gradients to answer a simple question: did this point survive past N iterations or not? This makes it easier to detect false interiors that only appear solid due to insufficient iteration depth or misleading smoothing.
- Palettes: Includes High Contrast (B/W) and Ghost Hunting alongside classic palettes to help in diagnostics.
- Navigation: drag to pan, mouse wheel to zoom (with double-click mode), Shift + drag for rectangle zoom selection, and optional center crosshair overlay to help in keeping the center in place.
- Utilities: Copy current and Home for fast state capture and return.
- Escape Gamma: Emphasizes late escapes to reveal potential “ghost” interior regions.
- Bailout control: Selectable escape radius (classic default is 2; higher values delay escape detection and can reveal additional boundary structure).
Limitations
- Speed at extreme depths: BigInt fixed‑point arithmetic is much slower than double precision (no perturbation/series acceleration techniques that would accelerate deep zoom rendering).
- High precision interaction restriction: In deep zoom mode, some pointer interactions are intentionally disabled to maintain numerical stability and rendering speed. That’s why zooming remains center-locked rather than following the cursor.
- Smooth coloring: In deep zoom mode, smooth escape coloring uses approximated values rather than exact calculations, which can affect gradient quality at extreme magnifications.
- Double-precision constraints: When high-precision mode is disabled, standard floating-point limits apply. At very small scales, coordinate precision breaks down and fine details can become blurred or “mushed out.”