Mathematics & Computing · Fractal Geometry

Quantify the Complexity Hidden in Nature

An interactive scientific tool for computing fractal dimensions of natural patterns using the box-counting method — underpinned by original academic research in fractal geometry.

11Specimens Analyzed
1.35–1.99Fractal Dimension Range
>0.99Average R² Score
3Analysis Modes

From Image to Fractal Dimension in 4 Steps

A rigorous OpenCV pipeline runs server-side for reproducibility and scientific accuracy.

01

Preprocess

Upload any image. Choose Full Mask, Boundary (Canny edge), or Texture (morphological gradient) extraction mode.

02

Threshold

Otsu auto-thresholding, adaptive localized, or manual — converts to a precise binary mask.

03

Box Count

Non-empty boxes counted across scales (powers of 2) with 4 grid offsets for maximum accuracy.

04

Regress

Log-log linear regression yields D and R². Confidence intervals and sensitivity analysis validate every result.

Built for Scientific Rigour

Reliability Dashboard

Every analysis returns a quality score (0–100), 95% confidence interval, standard error, and threshold sensitivity test.

Specimen Comparison Engine

Overlay your log-log regression line against 11 dissertation specimens on a shared auto-scaled D3 chart. ΔD computed instantly.

Algorithm Microscope

Watch the box-counting grid render live on the binary image at every scale. Step through each counting level interactively.

Multi-Mode Preprocessing

3 analysis modes × 3 threshold methods = 9 preprocessing combinations. Auto-reanalysis fires on every change with 600ms debounce.

Built With

Production-grade tools chosen for reproducibility and performance.

Frontend

Next.js 16React 19TypeScriptTailwind CSS v4D3.jsZustandFramer MotionSupabase JS

Backend

FastAPIPython 3.14OpenCVNumPySciPySupabase PostgreSQLUvicornslowapi

Data Flow Architecture

Browser
Next.js + Zustand
FastAPI + OpenCV
Supabase

Ready to Analyze Your First Image?

Upload a leaf, coastline, or any natural pattern. Results in seconds.

Launch Analyzer Lab