Complex TreesBernat Espigulé

Complex Trees · Project directory

Mathematics you
can explore.

A guide to my interactive research tools, mathematical images, and teaching projects. Each explorer connects a family of parameters with the geometry it produces. Recorded talks and historical presentations are collected in the talks & materials archive.

Detailed angular survey of the 4D atlas, with coloured bands of finite numerical signatures.

Research preview · 2026

4D Connectedness Atlas

Explore binary planar similarity families with four real parameters and direct or reversing similarities. Compare attractors and contacts, browse marked families in the Tip Atlas, or enter a parameter in the local explorer to inspect finite-depth overlaps and radial samples.

Open atlas ↗Tip AtlasLocal parameter explorerAngular survey & referenceMathematical guideDetailed laboratorySpecimen platesHigher-arity families

The thumbnail is the current angular-survey render. Its toroidal shape comes from the display projection. Finite-depth survival remains unresolved; the guide distinguishes numerical observations, validated computations and mathematical results.

Four coloured first-level pieces of a collinear self-similar set, captured from the current explorer.

Research software · 2026

Collinear Fractals Explorer

Explore collinear self-similar sets through linked parameter and dynamical views, geometric overlays, finite inverse searches, shareable configurations, and image export.

Open explorer ↗Source & documentationRelated preprint

Research explorer, version 0.2.0-alpha, with WebGL 2 previews and binary64 CPU refinement. The image shows four first-level pieces at c ≈ 1.5 + 1.6583123951777i. Finite searches provide numerical evidence within their stated limits; they do not by themselves prove connectedness.

Interactive paper companion · 2026

Sierpiński, Rauzy
& Apollonian gaskets

Compare an affine-projective interpolation from Sierpiński to Rauzy with a Möbius deformation from Sierpiński to Apollonian, through finite approximations and three-dimensional views.

Open the companion ↗Rauzy–Sierpiński 3D stackSierpiński–Apollonian 3D stackRead the preprintCite this work

Read, explore, compare.

The manuscript supplies the construction and proofs. The companion makes the changing geometry available for visual exploration.

Six yellow, blue and red 3D-printed complex trees in the 2019 Arboretum.

Art · sculpture · animation

Mathematical forms

Sculptures, computational drawings, animations, and geometric objects developed through Complex Trees. Each work includes its own context and exhibition record.

Visit the portfolio ↗Image credits & recordsICERM Math Cartography

Pictured: Arboretum of 3D-Printed Complex Trees, exhibited at ICERM in 2019. The portfolio records creation dates, exhibition dates and image sources separately.

Further resources

Recordings · slides · teaching

Talks & materials archive

Research talks on your choice of platform, downloadable materials, and historical Keynote presentations, indexed by year and topic.

Search the archive ↗YouTube channel ↗

Interactive exhibition

History of Mathematics

Learning journeys developed with Wolfram Research for the National Museum of Mathematics, New York.

Visit the exhibition ↗

Earlier research explorer

Collinear fractals · original GPU page

A preserved September 2026 snapshot of the earlier browser explorer. The old /collinear/ address now forwards to the maintained application.

Open the archived explorer ↗

Computational communication

Wolfram Blog

Eight articles written between 2014 and 2021, bringing computational experiments and mathematical ideas to a broad audience.

Read the articles ↗