The Heart of Mathematics: An Invitation to Effective Thinking
4th Edition
ISBN: 9781118156599
Author: Edward B. Burger, Michael Starbird
Publisher: Wiley, John & Sons, Incorporated
expand_more
expand_more
format_list_bulleted
Textbook Question
Chapter 7.4, Problem 35MS
Mandelbrot origins. Using your insights from Mindscapes 31-34, make a conjecture about an alternative description of the Mandelbrot Set that refers to the origin.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionChapter 7 Solutions
The Heart of Mathematics: An Invitation to Effective Thinking
Ch. 7.1 - The incredible shrinking duck. On the Quacked...Ch. 7.1 - Multiplicity (S). In the Sierpinski Triangle,...Ch. 7.1 - Different sizes. In the fern, find three reduced...Ch. 7.1 - Blooming broccoli. In the bunch of broccoli, find...Ch. 7.1 - Prob. 5MSCh. 7.1 - Prob. 6MSCh. 7.1 - Maybe moon. What features of the fractal forgeries...Ch. 7.1 - Exposing forgeries. What features of the fractal...Ch. 7.1 - Natures way. Find some examples of self-similarity...Ch. 7.1 - Do it yourself (H). Draw a figure that contains...
Ch. 7.1 - With a group of folks. In a small group, discuss...Ch. 7.1 - Prob. 12MSCh. 7.2 - A search for self. What does self-similarity mean?Ch. 7.2 - Desperately seeking similarity. Which of these...Ch. 7.2 - Too many triangles? At stage 0, the Sierpinski...Ch. 7.2 - Counting Koch. Look at the early stages of the...Ch. 7.2 - Argyle art. Take four line segments and place them...Ch. 7.2 - Natures way. Find several examples of objects in...Ch. 7.2 - Whos the fairest? Can you position three mirrors...Ch. 7.2 - Billiards and mirrors. On an idealized, square...Ch. 7.2 - MTV. Youve become a rock star and consequently...Ch. 7.2 - Photo op. Suppose you arrange two mirrors facing...Ch. 7.2 - How many mes? Arrange mirrors and camera as in...Ch. 7.2 - Quacker, Quacker, Quacker. Suppose you had the job...Ch. 7.2 - Sierpinski hexed (S). Take an equilateral triangle...Ch. 7.2 - The Kinks (ExH). Kochs kinky curve is created by...Ch. 7.2 - Four times (H). Draw a picture on a square piece...Ch. 7.2 - Burger heaven (S). Sketch a picture of a...Ch. 7.2 - Ice cream cones. Draw a picture of an ice cream...Ch. 7.2 - Sierpinski boundary. Take the boundary of a...Ch. 7.2 - Catching Zs (H). Take a Z. Put in nine smaller Zs,...Ch. 7.2 - Replacement pinwheel. Take a 1,2,2 right triangle....Ch. 7.2 - Koch Stool (ExH). Start with a line segment, mark...Ch. 7.2 - Koch collage stool. Given the Koch Stool described...Ch. 7.2 - Sierpinski shooting. Suppose that you were playing...Ch. 7.2 - Sierpinski target practice (H). What sequence of...Ch. 7.2 - Cantor Set. Start with the interval [0, 1]. Build...Ch. 7.2 - Cantor luck (H). Start with the point 0. Flip a...Ch. 7.2 - Cantor Square (S). Take a square. Make four...Ch. 7.2 - Cantor Square shrunk. Take the Cantor Square....Ch. 7.2 - Cantor Squared. Draw the four corners of a square,...Ch. 7.2 - Hexed again. Suppose you start with the three...Ch. 7.2 - Prob. 31MSCh. 7.2 - Antoines necklace. Antoines necklace is a delicate...Ch. 7.2 - Menger jacks. For the game of jacks, lets imagine...Ch. 7.2 - A tighter weave. Look back at the Tight Weave...Ch. 7.2 - A looser weave. Lets modify the carpet-designing...Ch. 7.2 - From where? Look at this fractal. What collage...Ch. 7.2 - Treed. Describe collage-making instructions that...Ch. 7.2 - Flaky (H). Describe collage making instructions...Ch. 7.2 - How big a hole? In the Tighter weave (34) and...Ch. 7.2 - 4D fractal. Describe a fractal in 4-dimensional...Ch. 7.2 - Personal perspectives. Write a short essay...Ch. 7.2 - With a group of folks. In a small group, discuss...Ch. 7.2 - Graphing Koch. Plot the following points in the...Ch. 7.2 - Koch adds life. Look at the points given in the...Ch. 7.2 - White out. Each stage of the Sierpinski triangle...Ch. 7.2 - Measuring the length of your Koch. The Koch stool...Ch. 7.2 - Counting Koch segments (H). Suppose you start with...Ch. 7.3 - Parallel grams. At right we see a parallelogram....Ch. 7.3 - Moving on up. Heres a triangle along with some...Ch. 7.3 - Bigger rug. Heres a picture of the Sierpinski...Ch. 7.3 - Dimension connection. What equation relates the...Ch. 7.3 - Divining dimension. If a fractal object requires...Ch. 7.3 - Stay inbounds. Give two consecutive integers that...Ch. 7.3 - Regular things (H). Find the fractal dimension of...Ch. 7.3 - More regular things. Find the fractal dimension of...Ch. 7.3 - Any right triangle. Take any right triangle. It...Ch. 7.3 - Sierpinski carpet (S). Compute the fractal...Ch. 7.3 - Koch Stool. Compute the fractal dimension of the...Ch. 7.3 - Cantor Set (H). The Cantor Set was constructed by...Ch. 7.3 - Cantor reduced. Suppose you take a unit interval,...Ch. 7.3 - Long Koch (ExH). The first stage in the...Ch. 7.3 - Pius (H). This fractal plus sign is self-similar...Ch. 7.3 - Tiniler triangles (S). Suppose you make something...Ch. 7.3 - Menger Sponge (ExH). Compute the fractal dimension...Ch. 7.3 - Thinning. Take a square. Make two copies, each...Ch. 7.3 - Not much. What is the fractal dimension of the...Ch. 7.3 - Koched (H). Create a Koch-like curve with fractal...Ch. 7.3 - Find a fractal. Describe a fractal having...Ch. 7.3 - Prob. 22MSCh. 7.3 - Personal perspectives. Write a short essay...Ch. 7.3 - With a group of folks. In a small group, discuss...Ch. 7.3 - Prob. 25MSCh. 7.3 - Power beyond the mathematics. Provide several...Ch. 7.3 - Varying dimensions. Using any method, including...Ch. 7.3 - Dimensional thinking. The text defines the...Ch. 7.3 - Power play (H). Using any method, including...Ch. 7.3 - Marching madness. The marching band wants to...Ch. 7.3 - More marching madness. For the second drill in the...Ch. 7.4 - Not Raul. Who was Gaston Julia?Ch. 7.4 - Use your imagination. What does the number i...Ch. 7.4 - Complex plots. The complex number 3+2i is plotted...Ch. 7.4 - Prob. 4MSCh. 7.4 - Outie or innie? If you use the point a+bi to build...Ch. 7.4 - Arithmetic. Compute the following sums and...Ch. 7.4 - More arithmetic (ExH). Compute the following sums...Ch. 7.4 - Quick draw. Two complex numbers are marked and...Ch. 7.4 - III iterate I (12:S). Feeling queasy? Then compute...Ch. 7.4 - III iterate I (12:S). Feeling queasy? Then compute...Ch. 7.4 - III iterate I (12:S). Feeling queasy? Then compute...Ch. 7.4 - III iterate I (12:S). Feeling queasy? Then compute...Ch. 7.4 - III iterate II (18:S). Compute the first three...Ch. 7.4 - III iterate II (18:S). Compute the first three...Ch. 7.4 - III iterate II (18:S). Compute the first three...Ch. 7.4 - III iterate II (18:S). Compute the first three...Ch. 7.4 - 1III iterate III. Compute the first three iterates...Ch. 7.4 - III iterate III. Compute the first three iterates...Ch. 7.4 - III iterate III. Compute the first three iterates...Ch. 7.4 - III iterate III. Compute the first three iterates...Ch. 7.4 - Orange Julias. Pictured here are some Julia Sets...Ch. 7.4 - Julia Webbed. Visit the Heart of Mathematics Web...Ch. 7.4 - Great escape? For each of the complex...Ch. 7.4 - Great escape? For each of the complex numbers...Ch. 7.4 - Great escape? For each of the complex numbers...Ch. 7.4 - Mandelbrot or not? (H). The images on the...Ch. 7.4 - Mandelbrot or not? (H). The images on the...Ch. 7.4 - Zero in (S). For each picture of the Julia Sets in...Ch. 7.4 - Zero in (S). For each picture of the Julia Sets in...Ch. 7.4 - Zero in (S). For each picture of the Julia Sets in...Ch. 7.4 - Zero in (S). For each picture of the Julia Sets in...Ch. 7.4 - Mandelbrot origins. Using your insights from...Ch. 7.4 - Prob. 36MSCh. 7.4 - Bounded Julia (ExH). Why is no Julia Set...Ch. 7.4 - Prisoner. Find a complex number a+bi that is fixed...Ch. 7.4 - Mandelbrot connections. Can every two points on...Ch. 7.4 - Personal perspectives. Write a short essay...Ch. 7.4 - With a group of folks. In a small group, discuss...Ch. 7.4 - Power beyond the mathematics. Provide several...Ch. 7.4 - Quadratic complexity (H). The quadratic formula...Ch. 7.4 - Special products. Compute the following products...Ch. 7.4 - Somethings fishy. The treasurer of the Marine...Ch. 7.4 - On the line. In the xy-plane, sketch the graph of...Ch. 7.4 - A line with a complex. Plot the points in the...Ch. 7.5 - Any interest? Suppose you put $1000 in a bank...Ch. 7.5 - Urban expansion. In the year 2004 the village of...Ch. 7.5 - Pre-sushi. Suppose a pond can sustain a maximum of...Ch. 7.5 - A booby trap. A small landmass off the Galapagos...Ch. 7.5 - Too many. The island of Birdburg has an area of...Ch. 7.5 - Call your shots. For each picture below, trace the...Ch. 7.5 - Getting cornered. Starting from the spot indicated...Ch. 7.5 - Double your money (H). Suppose you I deposit $1000...Ch. 7.5 - Too many(S). Earths surface is approximately...Ch. 7.5 - Rice bowl (H). One day long ago, the Emperor of...Ch. 7.5 - Natures way. Find some examples, other than those...Ch. 7.5 - The Game of Life (12:S). For each initial...Ch. 7.5 - The Game of Life (12:S). For each initial...Ch. 7.5 - The Game of Life (12:S). For each initial...Ch. 7.5 - The Game of Life (12:S). For each initial...Ch. 7.5 - Life cycles. For each initial population in the...Ch. 7.5 - Life cycles. For each initial population in the...Ch. 7.5 - Life cycles. For each initial population in the...Ch. 7.5 - Life cycles. For each initial population in the...Ch. 7.5 - Explosion. Devise a new initial population in the...Ch. 7.5 - Extinction. Construct a new initial population in...Ch. 7.5 - Periodic population (H). Construct a new initial...Ch. 7.5 - Programmed population. On a computer or...Ch. 7.5 - Programmed population: the next generation. Using...Ch. 7.5 - How many now? Suppose that a population is modeled...Ch. 7.5 - Fibonacci. Fibonacci numbers are constructed using...Ch. 7.5 - Fibonacci again. For each of the two columns you...Ch. 7.5 - Prob. 29MSCh. 7.5 - Cobweb plots (ExH). Here we visualize the...Ch. 7.5 - More spiders (S). Here is the graph of...Ch. 7.5 - Arachnids. Here is the graph of y=4x(1x). Start on...Ch. 7.5 - Making dough. Many delicious French desserts, such...Ch. 7.5 - Making dough. Many delicious French desserts, such...Ch. 7.5 - Making dough. Many delicious French desserts, such...Ch. 7.5 - More cobwebs (H). Consider the inverted V graph...Ch. 7.5 - Yet more cobwebs. Given the inverted V graph...Ch. 7.5 - Cantors cuts. Start with the unit interval [0, 1]....Ch. 7.5 - How much ¡s gone? In the construction of the...Ch. 7.5 - How much remains? Consider numbers that are not in...Ch. 7.5 - Personal perspectives. Write a short essay...Ch. 7.5 - With a group of folks. In a small group, discuss...Ch. 7.5 - Prob. 43MSCh. 7.5 - Power beyond the mathematics. Provide several...Ch. 7.5 - Life happens. A particular starting configuration...Ch. 7.5 - Perplexing population predictions. Verhulst model...Ch. 7.5 - More prediction peril. Consider the previous...Ch. 7.5 - Cobweb parabola. Mindscapes 3032 describe cobweb...Ch. 7.5 - Two sad and one happy parabolas. Building on your...Ch. 7.6 - Does this thing come with a warranty? If you use...Ch. 7.6 - Root repeater. Find a calculator with a square...Ch. 7.6 - Transforming experience. The equation y=4x(1x) is...Ch. 7.6 - Up and over. In this graph, we see a red diagonal...Ch. 7.6 - Over and up. Here is a simpler version of the...Ch. 7.6 - The cobweb tent (ExH). Take a square in which the...Ch. 7.6 - The cobweb tent (ExH). Take a square in which the...Ch. 7.6 - The cobweb tent (ExH). Take a square in which the...Ch. 7.6 - The cobweb tent (ExH). Take a square in which the...Ch. 7.6 - The cobweb tent (ExH). Take a square in which the...Ch. 7.6 - The cobweb tent (ExH). Take a square in which the...Ch. 7.6 - The cobweb tent (ExH). Take a square in which the...Ch. 7.6 - The cobweb tent (ExH). Take a square in which the...Ch. 7.6 - The cobweb tent (ExH). Take a square in which the...Ch. 7.6 - The cobweb tent (ExH). Take a square in which the...Ch. 7.6 - The cobweb tent (ExH). Take a square in which the...Ch. 7.6 - The cobweb tent (ExH). Take a square in which the...Ch. 7.6 - The cobweb tent (ExH). Take a square in which the...Ch. 7.6 - Too high. Consider a tent function that got too...Ch. 7.6 - More gone. In the too high tent function in the...Ch. 7.6 - Too short. Consider a short tent function. Will...Ch. 7.6 - Where to? Using the transformation y=3.5x(1x),...Ch. 7.6 - Calculator slips. Using the logistic...Ch. 7.6 - Take stock. Pick a stock. Some Web sites will...Ch. 7.6 - Repulsive. If you take the number 1 and square it,...Ch. 7.6 - Attractive. Again consider the process of repeated...Ch. 7.6 - Sierpinski attractor. Remember how the Sierpinski...Ch. 7.6 - Two step. Consider the transformation that takes...Ch. 7.6 - Periodic attraction (S). Again consider the...Ch. 7.6 - Periodic attraction. Again consider the...Ch. 7.6 - Four-peat (H). Consider the equation y=3.5x(1x)....Ch. 7.6 - Nearly fourly. Consider the equation y=3.5x(1x)....Ch. 7.6 - Tent attraction? Consider the point 0.4, which is...Ch. 7.6 - Becoming periodic. The point 0.4 is of period 2 in...Ch. 7.6 - The Earth moved (ExH). Consider a transformation...Ch. 7.6 - Poles apart. Consider the same transformation as...Ch. 7.6 - Logistic cobwebs. Lets explore the relatively...Ch. 7.6 - Logistic cobwebs. Lets explore the relatively...Ch. 7.6 - Logistic cobwebs. Lets explore the relatively...Ch. 7.6 - With a group of folks. In a small group, discuss...Ch. 7.6 - Power beyond the mathematics. Provide several...Ch. 7.6 - V-quation. Look at the graph for Mindscape 4. The...Ch. 7.6 - Meeting up. Look at the graph for Mindscape 38....Ch. 7.6 - We meet again. Look at the graph for Mindscape 39....Ch. 7.6 - Calculating percentages (H). Return to Table 1 on...Ch. 7.6 - Calculating percentages II. Repeat Mindscape 48...
Additional Math Textbook Solutions
Find more solutions based on key concepts
Checkpoint1
Use the substitution method to solve this system:
Answers to Checkpoint exercises are found at the...
Mathematics with Applications In the Management, Natural, and Social Sciences (12th Edition)
The equation ∂N∂t=∂2N∂r2+1r∂N∂r+kN
Fundamentals of Differential Equations and Boundary Value Problems
Find the additive inverse of each of the following integers. Write the answer in the simplest possible form. a....
A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)
Warm Up Exercises
In Exercises 1-6, fill in the blanks with an appropriate word, phrase or symbol(s).
1. The va...
A Survey of Mathematics with Applications (10th Edition) - Standalone book
Mixed Practice. In each of Problems through:
List each of the following classes into which the equation falls...
Differential Equations: An Introduction to Modern Methods and Applications
The expression fa when fx=x2−4x+9.
Finite Mathematics for Business, Economics, Life Sciences and Social Sciences
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.Similar questions
- Determine whether the set S={1,x2,2+x2} spans P2.arrow_forwardThe Mandelbrot Set A fractal is a geometric figure that consists of a pattern that is repeated infinitely on a smaller and smaller scale. The most famous fractal is the Mandelbrot Set, named after the Polish-born mathematician Benoit Mandelbrot (19242010). To draw the Mandelbrot Set, consider the sequence of numbers below. c,c2+c,(c2+c)2+c,[ (c2+c)2+c ]2+c,... The behavior of this sequence depends on the value of the complex number c. If the sequence is bounded (the absolute value of each number in the sequence, a+bi=a2+b2 is less than some fixed number N ), then the complex number c is in the Mandelbrot Set, and if the sequence is unbounded (the absolute value of the terms of the sequence become infinitely large), then the complex number c is not in the Mandelbrot Set. Determine whether the complex number c is in the Mandelbrot Set. (a)c=i (b)c=1+i (c)c=2 The figure below shows a graph of the Mandelbrot Set, where the horizontal and vertical axes represent the real and imaginary parts of c, respectively.arrow_forwardYOUR TURN Write the elements belonging to the set {x|xisastatewhosenamebeginswiththeletterO}.arrow_forward
Recommended textbooks for you
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageElementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,
- Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage LearningTrigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning
Calculus For The Life Sciences
Calculus
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:Pearson Addison Wesley,
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
Elementary Geometry For College Students, 7e
Geometry
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Cengage,
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:9781305658004
Author:Ron Larson
Publisher:Cengage Learning
Trigonometry (MindTap Course List)
Trigonometry
ISBN:9781337278461
Author:Ron Larson
Publisher:Cengage Learning
12. Searching and Sorting; Author: MIT OpenCourseWare;https://www.youtube.com/watch?v=6LOwPhPDwVc;License: Standard YouTube License, CC-BY
Algorithms and Data Structures - Full Course for Beginners from Treehouse; Author: freeCodeCamp.org;https://www.youtube.com/watch?v=8hly31xKli0;License: Standard Youtube License