Various fractals



In the “Fractal Catalog” iPhone/iPad app, you can see various fractal figures while moving them.

Fractals handled in “Fractal Catalog”

C Curve

Levy Curve, Levy C Curve

Sierpinski Gasket

Sierpinski Triangle, Sierpinski Sieve

Sierpinski Carpet



Sierpinski Curve

Hilbert Curve

Space-Filling Curve

Peano Curve

Space-Filling Curve

Moore Curve

Variant of Hilbert Curve : Space-Filling Curve


Koch Curve

Koch Snow Flake

Gumowski Mira Attractor

Gumowski Mira Attractor Parameter

Julia Set

Julia Set Parameter

Mandelbrot Set

Mandelbrot Set Parameter

Cellular Automaton

rule 7

rule 13

rule 30

rule 57

rule 90

rule 110

rule 129

Pascal’s Triangle

Barnsley Fern

Affine Transformation IFS

Barnsley Fern Determinant

Dragon Curve

Modified Koch Curve

Modified Koch Curve Parameter

Tree Curve

Tree Curve Parameter

Z Order Curve

Morton Order Curve, Lebesgue Curve

Minkowski Sausage

Vicsek Snow Flake Saltire

Box Fractal, Vicsek Fractal

Vicsek Snow Flake Cross

Box Fractal, Vicsek Fractal

Torn Square Fractal

Cesaro fractal

Torn Square Fractal Parameter

Cantor Set

Cantor Dust


Gosper Curve

N = 7

Gosper Curve N13

N = 13

Affine Transformation IFS Ammonite

Affine Transformation IFS Ammonite Determinant

Affine Transformation IFS Tree

Affine Transformation IFS Tree Determinant

Affine Transformation IFS Twin Dragon

Affine Transformation IFS Twin Dragon Determinant

Affine Transformation IFS Branch

Affine Transformation IFS Branch Determinant

Affine Transformation IFS Fern 2

Affine Transformation IFS Fern 2 Determinant

Chaos Game

Random Game

Chaos Game Parameter

Random Walk & Levy Flight

Random Walk & Levy Flight Parameter

Diffusion Limited Aggregation

Diffusion Limited Aggregation Parameter

Diffusion Limited Deposition

Diffusion Limited Deposition Parameter

Invasion Percolation


Ballistic Aggregation

BA Diffusion Limited Aggregation

Ballistic Aggregation Parameter

Devil’s Staircase

Cantor Function

Eden Model

Scheidagger River Net

How to use “Fractal Catalog”

Fractal List

Tap the “Start” button on the startup screen to display the Fractal List.


To change the fractal order, tap the “Edit” button at the bottom left of the “Fractal List Screen”.

If you tap the “i” button that appears when you tap a row, you will transition to the individual fractal screen.

Save fractal image

The “Individual Fractal Screen” has a “Save Image” button and a “transparent” switch.

Tap the “Save Image” button to save the fractal image displayed at that time. Saved images can be shared with the sharing function (email, AirDrop, etc.) of the “File” app.

If the “transparent” switch is on, the white areas of the saved image will be transparent.

“Fractal Catalog” App Store

App Store

Fractal Catalog