FRACTAL TRIPEXPLORE INFINITYTAKE A TRIP ✦
GET DISTRACTED

Strange Math & Visual Science

Infinity, chaos, giant numbers, impossible geometry and scientific rabbit holes.

VISUALRESEARCHEDDEEP DIVE
Strange Math & Visual Science fractal artwork
Original Fractal Trip procedural render
GET DISTRACTED

Strange Math & Visual Science

INFINITY

Some infinities are larger

Cantor changed what “infinite” means.

OPEN →CHAOS

Exact rules become unpredictable

Sensitive dependence from deterministic equations.

OPEN →PI

π appears in Mandelbrot iterations

A wild claim with real mathematics behind it.

OPEN →DIMENSION

A curve can be 1.26186-dimensional

Scale can live between dimensions.

OPEN →DEEP

10^10000 is an address problem

Precision dominates extreme zoom.

OPEN →3D

Equations become architecture

Ray marching implicit worlds.

OPEN →
A boundary with dimension 2The Mandelbrot boundary has Hausdorff dimension 2.
Escape radius 2 is enoughFor z²+c, once |z| exceeds 2 the orbit cannot return to bounded behavior.
The real slice is simpleThe Mandelbrot set intersects the real axis exactly from −2 to 1/4.
Every c defines a Julia worldFix c and the same quadratic iteration defines a corresponding Julia dynamical system.
Connectedness has a mapFor z²+c, c lies in Mandelbrot exactly when the filled Julia set is connected.
Koch has infinite lengthThe Koch curve has infinite length while fitting in a bounded region.
Finite area, infinite perimeterThe Koch snowflake encloses finite area while its perimeter diverges.
Menger loses all volumeThe Menger sponge volume tends to zero despite endlessly increasing structure.
A fern fits in four transformsThe Barnsley fern emerges from four affine maps chosen probabilistically.
Newton makes fractalsRoot-finding basins can have fractal boundaries.
Buddhabrot plots journeysIt accumulates paths taken by escaping Mandelbrot orbits.
Mandelbulb is not “the” 3D MandelbrotThere is no unique canonical 3D analogue of complex numbers.
Power 8 became iconicThe n=8 Mandelbulb is famous for lobes and cavernous detail.
Deep zoom is a precision fightPast double precision, coordinate representation becomes a central problem.
Perturbation reuses expensive workOne high-precision reference orbit can serve many nearby pixels.