Skip to the sheet
Drawn Mathematics

Mathematics you can see, draw, and fold.

Category 02 of 05

Fractal Construction

Classic fractals built step by step from their rules, how their dimension is measured, and where nature approximates them only over a measured range of scales.

3 entries

  • A 1743 engraved map of Great Britain and Ireland with a decorative title block, a degree scale around the border and an inset of the northern islands.

    Fractal Construction

    Coastline Paradox: Seven Rulers, Seven Lengths for Britain

    On one 1:10m map, a 200 km ruler measures Great Britain's coast at 2,508 km and a 3.125 km ruler at 6,579 km. Walk it yourself and see where the rule stops.

    Image credit

    "Kaart van Groot-Brittannië en Ierland" by Christiaan Sepp, published by Isaak Tirion — https://commons.wikimedia.org/wiki/File:Kaart_van_Groot-Brittanni%C3%AB_en_Ierland,_RP-P-1937-1763.jpg — Public domain (printmaker Christiaan Sepp (c. 1720–1775) and publisher Isaak Tirion (1705–1769), dates per Library of Congress name authorities; published in Amsterdam in 1743; PD worldwide (US: published before 1930; EU: the makers died more than 70 years ago); museum image released into the public domain by the Rijksmuseum (RP-P-1937-1763; CC0 on Commons)); modified: cropped to just outside the engraved border, removing the paper margins and a pencilled inventory number; colours not altered

  • Illustration of a sheet of graph paper with a faint, half-erased pencil smudge on a green drafting table, with a pencil lying above it and a brass compass beside it.

    Fractal Construction

    Sierpinski Triangle: A Dice Game Draws It Dot by Dot

    Roll a die, jump halfway to a corner, mark a dot: the dots fill in a Sierpinski triangle. See 10,000 dots, Pascal's odd numbers and its dimension, about 1.585.

    Image credit

    Illustration: Drawn Mathematics. Generated scene illustration — not a photograph, historical image or researched reconstruction. Use terms: may be reused with credit to "Drawn Mathematics"; provided without any claim of historical accuracy.

  • Illustration of a half-opened folded paper strip lifting in soft bends on a green drafting table, with a pencil in front of it and a small blank sheet of paper behind.

    Fractal Construction

    Dragon Curve: Fold a Strip, Open to 90°, and a Stage Appears

    Fold a paper strip in half again and again, open every crease to 90°, and it traces a stage of the dragon curve. Checked to 16 folds: no edge used twice.

    Image credit

    Illustration: Drawn Mathematics. Generated scene illustration — not a photograph, historical image or researched reconstruction. Use terms: may be reused with credit to "Drawn Mathematics"; provided without any claim of historical accuracy.