This document discusses fractals and some examples of fractal patterns and curves. It describes a fractal as a mathematical set that displays self-similar patterns at different scales. Specific fractals mentioned include the Sierpinski triangle, Koch curve, and Koch snowflake. The Koch snowflake, also known as the Koch star or Koch island, is constructed iteratively by adding triangles to the sides of an initial triangle shape.

1. Fractal
• A fractal is a mathematical set that
typically displays self-similar patterns,
which means they are "the same from
near as from far"

2. Natural phenomena with fractal
features

3. fractal in architecture

4. Sierpinski triangle
• Originally constructed as a curve, this is one of
the basic examples of self-similar sets, i.e. it is
a mathematically generated pattern that can
be reproducible at any magnification or
reduction

5. Construction
of
Sierpinski triangle

7. The Koch Curve

8. we see the third order Koch island
(or snowflake)

9. is the fifth order Koch curve, magnified
four times

10. The sixth order Koch curve

11. The Koch snowflake
• The Koch snowflake (also known as the Koch star
and Koch island[1]) is a mathematical curve and
one of the earliest fractal curves to have been
described. It is based on the Koch curve, which
appeared in a 1904 paper titled "On a continuous
curve without tangents, constructible from
elementary geometry" (original French title: Sur
une courbe continue sans tangente, obtenue par
une construction géométrique élémentaire) by
the Swedish mathematician Helge von Koch.

12. Construction
of
Snowflake

13. MADE BY:-
Nikhil Chaurasiya
And
Vipin Bhatt