Question 1 rs marks] {a} Briefly.r research what fractals are and summarise your findings in approximately zoo words including: ' a definition of fractals ' at least three appropriate examples at least one application of fractals. {b} In fractal geometry the terms Iteratr'onl escape set and prisoner set are used frequently. Write a definition for each of these terms. Question 2 - Exploring IFS Fractals {5 Marks) iterated Function System Fractats [IFS fractals) are created using simple plane geometry transformations such as enlargement, rotation, translation and dislocation that are applied to simple geometric figures. Wellknown fractals of this type include the Sierpinski triangle and the Koch Snowflake. (a) Watch the video: Building a Koch Snowflake. {b} Download triangular graph paper and use itto construct a Koch Snowflake that illustrates three iterations. Limit the size of your snowflake to fit on an A4 sheet of paper. . .. . . _ S {c} Prove that the lImItIng value of the area of a Koch Snowflake Is given by 1'1 119 where A\" is the area otthe initial triangle. Question 3 Complex Numbers and the Mandelbrot Set {it marks} {a} Watch the video: The Mandelbrot Set- Numberphile and read the article: Unveiling the Mandelbrot Set. Write a brief description of the Mandelbrot set. Limit your response to 100 words. tn} Consider the function filze=zZ+II1i { Beginning with 2:0 , calculate the values of 11,31. 23 and Z4 , the results after four iterations of the function. {iii Illustrate these five numbers on an Argand diagram. Label each number clearly