# Fractal ## MicroSim spec - **Recommended sim type:** fractal / iteration - **Microsimmability score:** 90/100 - **Layout:** drawing region (canvas) on top; control region (sliders/buttons) below. ### Parameters (tunable controls) - `Iteration depth` - `Branch angle` - `Scale ratio` ### What animates A self-similar shape is drawn recursively, adding finer detail at each iteration. ### Learning objective Show how iterating a simple rule produces self-similar fractal structure. ## MicroSim spec - **Recommended sim type:** fractal / iterative [[Geometry|geometry]] - **Microsimmability score:** 88/100 - **Layout:** drawing region (canvas) on top; control region (sliders/buttons) below. ### Parameters (tunable controls) - `Iterations` - `Branch angle` - `Scale ratio` ### What animates A self-similar shape unfolds with finer detail as iterations and angle change. ### Learning objective Show how repeating a rule across scales builds a fractal. ## Links (Wikipedia order) <!-- injected from _registry/childlinks/Fractal.json (2026-07-30T02:09:12Z) --> `4-polytope` · `5-cell` · `A_Mathematician's_Apology` · `A_Treatise_on_Painting` · `Absolute_geometry` · `Actin` · `Adolf_Zeising` · `Affine_geometry` · `African_art` · `Ahmes` · `Alan_Turing` · `Alba_Rojo_Cama` · `Albrecht_Dürer` · `Aleksandr_Lyapunov` · `Alessandra_Carbone` · `Algae` · `Algebraic_geometry` · [[Algorithm]] · `Algorithmic_art` · `Algorithmic_composition` · `Altitude_(triangle)` · `Amie_Wilkinson` · `Analytic_geometry` · `Anamorphosis` · `Anatoly_Fomenko` · `Andrea_Palladio` · `Anduriel_Widmark` · `Andy_Lomas` · `Angle` · `Animal_coloration` · `Anosov_diffeomorphism` · `Anthony_Hill_(artist)` · `Antoine_Pevsner` · `Apollonian_gasket` · `Apollonius_of_Perga` · `Archaeology` · `Archimedes` · [[Architecture]] · `Architecture_of_Africa` · `Area` · `Area_of_a_circle` · `Aristid_Lindenmayer` · `Arithmetic_geometry` · `Arnold's_cat_map` · `Arnold_tongue` · `Ars_Mathematica_(organization)` · `Art_Tower_Mito` · `Arthur_C._Clarke` · `Artifact_(error)` · `Aryabhata` · `Assouad_dimension` · [[Attractor]] · `Audrey_Terras` · `Axiom_A` · `Axiomatic_system` · `Baker's_map` · `Ball` · `Barnsley_fern` · `Barycentric_subdivision` · `Bathsheba_Grossman` · `Batik` · `Baudhayana` · `Benoit_Mandelbrot` · `Bernard_Bolzano` · `Bernhard_Riemann` · `Bifurcation_diagram` · [[Bifurcation_theory]] · `Bill_Gosper` · `Biology` · `Blaise_Pascal` · `Blancmange_curve` · `Blood_vessel` · `Body_proportions` · `Box_counting` · `Brahmagupta` · `Branching_process` · `Brefeldia_maxima` · `Brosl_Hasslacher` · `Brownian_motion` · `Brownian_motor` · `Brownian_tree` · `Bryna_Kra` · `Buddhabrot` · `Burning_Ship_fractal` · `Butterfly_effect` · `Cambridge,_Massachusetts` · `Camera_lucida` · `Camera_obscura` · `Camouflage` · `Cantor_set` · `Carl_Friedrich_Gauss` · `Caroline_Series` · `Catenary` · `Cathedral_of_Saint_Mary_of_the_Assumption_(San_Francisco)` · `Cell_division` · `Celso_Grebogi` · `Celtic_knot` · `Chaos:_Making_a_New_Science` · `Chaos_game` · [[Chaos_theory]] · `Charles_Jencks` · `Chen_Guanrong` · [[Christiaan_Huygens]] · `Chua's_circuit` · `Circadian_rhythm` · `Circle` · `Circle_Limit_III` · `Circular_triangle` · `Circumference` · `Clifford_A._Pickover` · `Coast` · `Coastline_paradox` · `Complex_geometry` · `Complex_plane` · `Complex_quadratic_polynomial` · [[Complexity]] · `Computational_geometry` · `Computer_art` · `Computer_graphics` · `Cone` · `Conformal_geometry` · `Congruence_(geometry)` · `Conservative_system` · `Continuous_function` · `Continuum_(sculpture)` · `Control_of_chaos` · `Convex_geometry` · `Coordinate_system` · `Correlation_dimension` · [[Coupled_map_lattice]] · `Croatian_interlace` · `Crockett_Johnson` · `Crucifixion_(Corpus_Hypercubus)` · `Crystal` · [[Crystal_structure]] · `Cube` · `Cuboid` · `Curve` · `Cymatics` · `D'Arcy_Wentworth_Thompson` · `DNA` · `Daina_Taimiņa` · `Dancer_in_a_Café` · `David_Foster_Wallace` · `David_Hilbert` · `David_Ruelle` · `De_Rham_curve` · `De_architectura` · `De_pictura` · `De_prospectiva_pingendi` · `De_re_aedificatoria` · `Decalcomania` · `Dendrite_(crystal)` · `Desmond_Paul_Henry` · `Determinism` · `Diagonal` · `Diameter` · `Diamond-square_algorithm` · `Diego_Krapf` · `Differentiable_function` · `Differential_geometry` · `Diffusion-limited_aggregation` · `Digital_geometry` · `Digital_sundial` · `Diophantine_geometry` · `Discrete_differential_geometry` · `Discrete_geometry` · `Disk_(mathematics)` · `Distance` · `Divina_proportione` · `Divination` · `Dodecahedron` · `Douady_rabbit` · `Double_pendulum` · `Douglas_Hofstadter` · `Dragon_curve` · `Droste_effect` · `Duffing_equation` · `Duffing_map` · `Dune` · `Dyadic_transformation` · `Dynamical_billiards` · [[Dynamical_system]] · `Edge_of_chaos` · [[Edward_Norton_Lorenz]] · `Edward_Ott` · `Einar_Thorsteinn` · `Elastic_pendulum` · `Elliptic_curve` · `Elliptic_geometry` · [[Emergence]] · `Empedocles` · `Endoplasmic_reticulum` · `Ergodic_theory` · `Ergodicity` · `Erik_Demaine` · `Ernest_Hanbury_Hankin` · `Ernst_Haeckel` · `Euclid` · `Euclid's_Elements` · `Euclidean_geometry` · `Euclidean_space` · `European_Society_for_Mathematics_and_the_Arts` · `Exponential_map_(discrete_dynamical_systems)` · `Feigenbaum_function` · `Felix_Hausdorff` · `Felix_Klein` · `Fermi–Pasta–Ulam–Tsingou_problem` · `Fern` · `Fibonacci` · `Fibonacci_word_fractal` · `Filippo_Brunelleschi` · `Filled_Julia_set` · `Finite_geometry` · `Finite_subdivision_rule` · `Floral_symmetry` · `Floris_Takens` · [[Fluid_dynamics]] · `Foam` · `Form_constant` · `Formula` · `Foundations_of_geometry` · `Four-dimensional_space` · `Fourth_dimension_in_art` · `Fractal-generating_software` · `Fractal_(disambiguation)` · `Fractal_analysis` · `Fractal_antenna` · `Fractal_art` · `Fractal_canopy` · `Fractal_compression` · `Fractal_cosmology` · `Fractal_curve` · `Fractal_derivative` · `Fractal_dimension` · `Fractal_dimension_on_networks` · `Fractal_flame` · `Fractal_in_soil_mechanics` · `Fractal_landscape` · `Fractal_sequence` · `Fractal_string` · `Fractalgrid` · `Fractography` · `Fracton` · `Fracture` · [[Fracture_mechanics]] · `Frederik_Macody_Lund` · `Frond` · `G._H._Hardy` · `Gaston_Julia` · `Gauss_iterated_map` · `Generalized_trigonometry` · `Geodesic` · `Geodesic_dome` · `Geography` · `Geometric_algebra` · `Geometric_analysis` · `Geometric_group_theory` · `Geometric_measure_theory` · [[Geometry]] · `Geometry_of_numbers` · `Georg_Cantor` · `George_David_Birkhoff` · `George_W._Hart` · `Gerald_L._Alexanderson` · `Gingerbreadman_map` · `Giorgio_de_Chirico` · `Girih` · `Glossary_of_Riemannian_and_metric_geometry` · `Glossary_of_algebraic_geometry` · `Glossary_of_arithmetic_and_diophantine_geometry` · `Glossary_of_classical_algebraic_geometry` · `Glossary_of_differential_geometry_and_topology` · `Glossary_of_symplectic_geometry` · `Golden_ratio` · `Gosper_curve` · `Goudreau_Museum_of_Mathematics_in_Art_and_Science` · [[Graph_of_a_function]] · `Great_Pyramid_of_Giza` · `Great_circle` · `Greeble` · `Gödel,_Escher,_Bach` · `H.S.M._Coxeter` · `H_tree` · `Hagia_Sophia` · `Hamid_Naderi_Yeganeh` · `Harvard_University_Press` · `Hausdorff_dimension` · `Heart_sounds` · `Hee_Oh` · `Heinz-Otto_Peitgen` · `Helaman_Ferguson` · `Helge_von_Koch` · `Henri_Poincaré` · `Hermann_Minkowski` · `Higuchi_dimension` · `Hilbert_curve` · `Hinke_Osinga` · `Hiroshi_Sugimoto` · `Histopathology` · `History_of_geometry` · `Hokky_Situngkir` · `Homeomorphism` · `Homunculus` · `Horseshoe_map` · `Hyperbolic_geometry` · `Hyperbolic_triangle` · `Hyperboloid_structure` · `Hypercube` · `Hypotenuse` · `Hénon_map` · `Hénon–Heiles_system` · `I_quattro_libri_dell'architettura` · `Ibn_al-Yasamin` · `Icosahedron` · `Ikeda_map` · `Impact_crater` · `In_silico` · `Incidence_geometry` · `Infinite_Jest` · `Infinite_regress` · `Information_geometry` · `Institute_For_Figuring` · `Integer` · `Interlace_(art)` · `Interval_exchange_transformation` · `Invariant_measure` · `Irrational_rotation` · `Islamic_geometric_patterns` · `István_Orosz` · `Itamar_Procaccia` · `Iterated_function_system` · `Iteration` · `Jackson_Pollock` · `Jali` · `James_A._Yorke` · `Jan_Dibbets` · `Jay_Hambidge` · `Jean_Metzinger` · `Jeanette_McLeod` · `John_Ernest` · `Joseph_Plateau` · `Journal_of_Mathematics_and_the_Arts` · `Julia_set` · `Jyeṣṭhadeva` · `János_Bolyai` · `Kaleidoscope` · `Kaplan–Yorke_map` · `Karl_Weierstrass` · `Kicked_rotator` · `Kite_(geometry)` · `Knot` · `Koch_snowflake` · `Kresge_Auditorium` · `Krylov–Bogolyubov_theorem` · `Kármán_vortex_street` · `Kātyāyana` · `L-system` · `Lacunarity` · `Lai-Sang_Young` · `Lake` · `Langton's_ant` · `Lebesgue_covering_dimension` · `Length` · `Leon_Battista_Alberti` · `Leon_O._Chua` · `Leonardo_da_Vinci` · `Leonhard_Euler` · `Lewis_Fry_Richardson` · `Liber_Abaci` · `Library_of_Congress` · `Lichtenberg_figure` · `Life` · `Lightning` · `Limit_set` · `Line_(geometry)` · `Line_segment` · `Liouville's_theorem_(Hamiltonian)` · `List_of_chaotic_maps` · `List_of_combinatorial_computational_geometry_topics` · `List_of_differential_geometry_topics` · `List_of_formulas_in_Riemannian_geometry` · `List_of_formulas_in_elementary_geometry` · `List_of_fractals_by_Hausdorff_dimension` · `List_of_geometers` · `List_of_knot_theory_topics` · `List_of_mathematical_artists` · `List_of_numerical_computational_geometry_topics` · `List_of_polygons` · `List_of_works_designed_with_the_golden_ratio` · [[Logarithmic_spiral]] · `Logistic_map` · `Loren_Carpenter` · `Lorenz_system` · `Lotka–Volterra_equations` · `Luca_Pacioli` · `Lumen_Naturae` · `Lyapunov_exponent` · `Lyapunov_fractal` · [[Lyapunov_stability]] · `Lévy_C_curve` · `Lévy_flight` · `M._C._Escher` · `MARPAT` · `Mackey–Glass_equations` · `Making_Mathematics_with_Needlework` · `Man_Ray` · `Manava` · `Mandelbox` · `Mandelbrot_set` · `Mandelbulb` · `Manifold` · `Marcelo_Viana` · `Margaret_Wertheim` · `Martin_Demaine` · `Martin_Gutzwiller` · `Martin_Ostoja-Starzewski` · [[Mary_Cartwright]] · `Mary_Rees` · `Mary_Tsingou` · `Mathemalchemy` · `Mathematica:_A_World_of_Numbers..._and_Beyond` · `Mathematical_beauty` · `Mathematical_sculpture` · `Mathematics` · `Mathematics_and_architecture` · `Mathematics_and_art` · `Mathematics_and_fiber_arts` · `Mathematics_of_paper_folding` · `Matryoshka_doll` · `Max_Bill` · `Max_Ernst` · `Meander` · `Measure-preserving_dynamical_system` · `Menger_sponge` · `Michael_Atiyah` · `Michael_Barnsley` · `Michael_Berry_(physicist)` · `Michael_Silverblatt` · `Michaelis–Menten_kinetics` · `Michel_Hénon` · `Mikhael_Gromov_(mathematician)` · `Mimicry` · `Minggatu` · `Minimal_surface` · `Minkowski_sausage` · `Minkowski–Bouligand_dimension` · `Misiurewicz_point` · `Mitchell_Feigenbaum` · `Mixing_(mathematics)` · `Monir_Shahroudy_Farmanfarmaian` · `Moore_curve` · `Mountain` · `Multibrot_set` · `Multifractal_system` · `Multiscroll_attractor` · `Muqarnas` · `Music_and_mathematics` · `N-flake` · `N-sphere` · `Nasir_al-Din_al-Tusi` · `National_Museum_of_Mathematics` · `Natural_selection` · `Nelson_Saiers` · `NeuroImage` · `Neuron` · [[Neuroscience]] · `Newton_(Blake)` · `Newton_fractal` · `Nikolai_Lobachevsky` · `Nikos_Salingaros` · `Nina_Snaith` · `Non-Archimedean_geometry` · `Non-Euclidean_geometry` · `Noncommutative_algebraic_geometry` · `Noncommutative_geometry` · `Octacube_(sculpture)` · `Octahedron` · `Oliver_Sin` · `On_Growth_and_Form` · `One-dimensional_space` · `Orbit_(dynamics)` · `Orbit_trap` · `Ordered_geometry` · `Organelle` · `Origami` · `Ornament_(art)` · [[Orthogonality]] · `Oswald_Veblen` · `Otto_Rössler` · `Outer_billiards` · `Outline_of_geometry` · `Owen_Jones_(architect)` · `Oxford_English_Dictionary` · `PBS` · `Packing_dimension` · `Pantheon,_Rome` · `Paola_Vannucchi` · `Paolo_Uccello` · `Paraboloid` · `Parallel_(geometry)` · `Parallelogram` · `Parastichy` · `Parmigianino` · `Parthenon` · `Pathology` · [[Pattern_formation]] · `Pattern_recognition_(psychology)` · `Patterns_in_nature` · `Paul_Lévy_(mathematician)` · `Peano_curve` · [[Percolation]] · `Percolation_theory` · `Periodic_point` · `Perpendicular` · `Perspective_(graphical)` · `Peter_Forakis` · `Peter_Grassberger` · [[Phase_space]] · `Phyllotaxis` · [[Physics]] · `Physiology` · `Pi_(art_project)` · `Pi_in_the_Sky` · `Pickover_stalk` · `Piero_della_Francesca` · `Pierre_Fatou` · `Plastic_ratio` · `Plateau's_laws` · `Plato` · `Poincaré_recurrence_theorem` · `Poincaré–Bendixson_theorem` · `Point_(geometry)` · `Polygon` · [[Polyhedron]] · `Polykleitos` · [[Polytope]] · [[Population_dynamics]] · `Power_law` · [[Predictability]] · `Print_Gallery_(M._C._Escher)` · `Procedural_generation` · [[Projective_geometry]] · `Proportion_(architecture)` · `Protein` · `Psilomelane` · `Psychedelic_experience` · `Purkinje_cell` · `Pyramid` · `Pyramid_(geometry)` · `Pythagoras` · `Pythagoras_tree_(fractal)` · `Pythagorean_theorem` · `Quadrilateral` · `Quantum_chaos` · [[Quasicrystal]] · `Rabinovich–Fabrikant_equations` · `Radius` · `Random_walk` · `Rasterisation` · `Rayleigh–Bénard_convection` · `Recreational_mathematics` · `Rectangle` · `Recurrence_plot` · [[Recurrence_relation]] · `Recursion` · `Relativity_(M._C._Escher)` · `Rendering_(computer_graphics)` · `René_Descartes` · `René_Magritte` · `Rep-tile` · `Reptiles_(M._C._Escher)` · `Reuleaux_polygon` · `Reuleaux_tetrahedron` · `Reuleaux_triangle` · `Rhombus` · `Rhythm_of_Structure` · `Riemannian_geometry` · `Rings_of_Saturn` · `River` · `Robert_Longhurst` · `Roman_Verostko` · `Romanesco_broccoli` · `Ron_Eglash` · `Rufus_Bowen` · `Rössler_attractor` · `SIGGRAPH` · `Sacred_geometry` · `Sagrada_Família` · `Sakabe_Kōhan` · `Salvador_Dalí` · `Samuel_Colman` · `Santa_Fe_Institute` · `Santiago_Calatrava` · `Scaling_(geometry)` · `Scott_Draves` · `Search_and_rescue` · `Sebastiano_Serlio` · `Seismology` · `Self-Portrait_in_a_Convex_Mirror_(Parmigianino)` · `Self-avoiding_walk` · [[Self-organization]] · [[Self-reference]] · `Self-similarity` · `Sexual_selection` · `Shape` · `Shiing-Shen_Chern` · `Sierpiński_carpet` · `Sierpiński_curve` · `Sierpiński_triangle` · `Similarity_(geometry)` · `Simplex` · `Slime_mold` · `Soap_bubble` · `Soil_mechanics` · `Solid_geometry` · `Solid_of_revolution` · `Solnhofen_Limestone` · `Space-filling_curve` · `Space_(mathematics)` · `Spectral_geometry` · `Sphere` · `Spherical_geometry` · `Spherical_trigonometry` · `Square` · `Stability_theory` · `Stable_manifold` · `Stable_manifold_theorem` · `Standard_map` · `Stochastic` · `Straightedge_and_compass_construction` · `Strange_loop` · `String_art` · `String_figure` · `Subset` · `Surface_(mathematics)` · `Surface_area` · `Susan_Goldstine` · `Svetlana_Jitomirskaya` · `Swinging_Atwood's_machine` · `Sydney_Opera_House` · `Symmetry` · `Symmetry_in_biology` · `Symplectic_geometry` · `Synchronization_of_chaos` · `Synthetic_geometry` · [[Systems_theory]] · `T-shirt` · `T-square_(fractal)` · `TED_(conference)` · `Taj_Mahal` · `Takens's_theorem` · `Tent_map` · [[Tessellation]] · `Tesseract` · `Tetrahedron` · `Texture_mapping` · `The_Ancient_of_Days` · `The_Beauty_of_Fractals` · `The_Bridges_Organization` · `The_Chemical_Basis_of_Morphogenesis` · `The_Fractal_Dimension_of_Architecture` · `The_Fractal_Geometry_of_Nature` · `The_Human_Condition_(Magritte)` · `The_Swallow's_Tail` · `Three-body_problem` · `Three-dimensional_space` · `Tilt-A-Whirl` · `Timeline_of_geometry` · `Tinkerbell_map` · `Tony_Robbin` · `Topological_conjugacy` · `Trapezoid` · `Triangle` · `Triangle_center` · `Tricorn_(mathematics)` · `Trigonometry` · `Tropical_geometry` · `Turbulence` · `Turtle_graphics` · `Two-dimensional_space` · `Van_der_Pol_oscillator` · `Vastu_shastra` · `Vector_calculus` · `Vertex_(geometry)` · `Vicsek_fractal` · `Viewpoints:_Mathematical_Perspective_and_Fractal_Geometry_in_Art` · `Virasena` · `Visual_system` · `Vitruvian_Man` · `Vitruvius` · `Volume` · `Wacław_Sierpiński` · `Wallpaper_group` · `Waterfall_(M._C._Escher)` · [[Wave]] · [[Wayback_Machine]] · [[Weather_forecasting]] · `Weierstrass_function` · `Widmanstätten_pattern` · `Wiener_process` · `William_Blake` · `Wilson_Bentley` · `Wind_wave` · `Yakov_Sinai` · `Yang_Hui` · `Z-order_curve` · `Zaslavskii_map` · `Zellij` · `Zero-dimensional_space` · `Zhang_Heng` · `Élie_Cartan` > Canonical collision file — this slug is claimed by more than one room. Per-hub sections below; the registry points here. ## Geometry Fractal The Geometry room reached this slug from the GEOMETRY PORTAL worklist (row 35, S-geosweep-035, 2026-07-23). Fractals are the room's recursion wing: the Sierpiński triangle, Menger sponge, and Koch snowflake each carry a live three.js microsim and a fractal-dimension ledger; [[Logarithmic_spiral]] holds the smooth version of self-similarity. This file is the door between the rooms that share the word. - Read on Wikipedia: https://en.wikipedia.org/wiki/Fractal - On Wikitube: https://en.wikitube.io/wiki/Fractal ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Fractal) : [Wikitube](https://en.wikitube.io/wiki/Fractal) ## Previous hub tags Tree parents: [[Complex_system]] · [[Cybernetics]] · [[Dynamical_system]] · [[Emergence]] · [[Feedback]] · [[Self-organization]] · [[Systems_science]] · [[Systems_theory]]. Legacy hubs: none. --- *Sources: 3 legacy notes. Minted wave 1, 2026-07-30 (v1.6 order).*