What is a Fractal?

The image is know as?

• Barnsely Fern

• Fractals Shapes

• Plant

• Green Leaf

Answer explanation

The image is known as the Barnsley Fern, a famous example of a fractal that mimics the appearance of a natural fern. It is not just a plant or a green leaf, but specifically recognized for its fractal geometry.

Are hexagons self-similar? Can you form big hexagons out of smaller ones?

• Yes, hexagons are self-similar and you can form big hexagons out of smaller ones.

• No, hexagons are not self-similar and you cannot form big hexagons out of smaller ones.

• Hexagons are self-similar but you cannot form big hexagons out of smaller ones.

• Hexagons are not self-similar but you can form big hexagons out of smaller ones.

Answer explanation

Yes, hexagons are self-similar because they can be divided into smaller hexagons that are identical in shape. You can arrange smaller hexagons to form larger hexagons, confirming both aspects of the question.

What is a famous example of a fractal based on the self-similar shape of a triangle?

• Sierpinski Triangle

• Mandelbrot Set

• Koch Snowflake

• Cantor Set

Answer explanation

The Sierpinski Triangle is a well-known fractal that exhibits self-similarity through repeated removal of triangles, creating a pattern that resembles a triangle at every scale. It is the best example of a triangle-based fractal.

Which tool do you need to draw and colour the next two Sierpinski triangles in this series?

• sharp pencil and a ruler

• paintbrush and canvas

• computer and software

• pen and notebook

Answer explanation

To draw and color Sierpinski triangles accurately, a sharp pencil and a ruler are essential for precise lines and angles. Other tools like a paintbrush or computer software are not suitable for this geometric task.

What is the first step in creating an Apollonian gasket-style fractal?

• Start with a circle and then add three circles within it which are tangential to each other as well as to the outer circle.

• Begin with a square and inscribe four circles within it.

• Start with a triangle and place circles at each vertex.

• Draw a line and place circles along it.

Answer explanation

The first step in creating an Apollonian gasket is to start with a circle and then add three smaller circles inside it that are tangent to each other and to the outer circle, forming the basis of the fractal.

What makes the Apollonian gasket a fractal?

• You can keep on adding smaller and smaller circles into the spaces an infinite number of times.

• It is made up of only straight lines.

• It cannot be divided into smaller parts.

• It is a two-dimensional shape.

Answer explanation

The Apollonian gasket is a fractal because you can keep adding smaller circles into the gaps infinitely, creating an intricate pattern. This self-similar property is a key characteristic of fractals.

Who first described the Koch Snowflake?

• Helge von Koch

• Benoit Mandelbrot

• Georg Cantor

• Felix Hausdorff

Answer explanation

The Koch Snowflake was first described by Helge von Koch in 1904. He introduced this fractal curve as a mathematical concept, which later gained popularity in the study of fractals and geometry.

What is the first step in creating a Koch Snowflake?

• Start by drawing an equilateral triangle.

• Draw a square.

• Begin with a circle.

• Create a straight line.

Answer explanation

The first step in creating a Koch Snowflake is to start by drawing an equilateral triangle. This triangle serves as the foundation for the iterative process that defines the snowflake's unique fractal shape.

A fun variation of creating an Apollonian gasket-style fractal is:

• Using different colors for each circle

• Adding random noise to the circles

• Incorporating 3D elements

• All of the above

Answer explanation

All options enhance the Apollonian gasket-style fractal: using different colors adds visual interest, random noise introduces variation, and 3D elements create depth. Thus, 'All of the above' is the correct choice.

What is the name of the six-sided shape formed in the third stage of making a Koch snowflake?

• Hexagram

• Hexagon

• Pentagon

• Octagon

Answer explanation

In the third stage of creating a Koch snowflake, the shape formed is a hexagram, which consists of overlapping triangles creating a six-sided figure. The other options, like hexagon and pentagon, do not accurately describe this shape.