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Fractals the Secret Code of Creation
What if mathematicians discovered a secret code embedded in math disclosing an amazing work of art hidden in the numbers? Just such a code of astounding beauty was discovered in the 1980s. The artworks displayed in this book have always existed, built into the numbers at creation. Dr. Lisle suggests that only the Christian worldview can make sense of this secret code. As such, the images in this book are a demonstration of the truth of that worldview.
216 pages, Paperback
Published January 1, 2021
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94 people want to read
About the author
Jason Lisle
36 books116 followersDr. Jason Lisle is an astrophysicist who formerly worked for the creationist organization Answers in Genesis as both a speaker and researcher, but is now Director of Research at the Institute for Creation Research.
Dr. Lisle is a creationist who has a PhD in Astrophysics, which he obtained through the University of Colorado in Boulder. His postgraduate research concentrated on solar dynamics, utilizing NASA's Solar and Heliospheric Observatory (SOHO) to monitor the surface of the sun. His PhD dissertation "Probing the Dynamics of Solar Supergranulation and its Interaction with Magnetism." is available from the University of Colorado and he has also published numerous papers in scientific literature concerning convection cells in the sun.
Although some creationists claim, as in the film Expelled, that holding to creationist beliefs while pursing a degree at an accredited University will get you kicked out, Dr. Jason Lisle recieved his undergraduate degree from Ohio Wesleyan University summa cum laude with a double-major in physics and astronomy and a minor in mathematics. For his thesis and dissertation, (Master's and Ph.D accordingly,) though members of his Peer-Review Panel might have been aware of his young Earth beliefs - their evaluation of his work was based on his actual research and not his personal beliefs.
Dr. Lisle is a creationist who has a PhD in Astrophysics, which he obtained through the University of Colorado in Boulder. His postgraduate research concentrated on solar dynamics, utilizing NASA's Solar and Heliospheric Observatory (SOHO) to monitor the surface of the sun. His PhD dissertation "Probing the Dynamics of Solar Supergranulation and its Interaction with Magnetism." is available from the University of Colorado and he has also published numerous papers in scientific literature concerning convection cells in the sun.
Although some creationists claim, as in the film Expelled, that holding to creationist beliefs while pursing a degree at an accredited University will get you kicked out, Dr. Jason Lisle recieved his undergraduate degree from Ohio Wesleyan University summa cum laude with a double-major in physics and astronomy and a minor in mathematics. For his thesis and dissertation, (Master's and Ph.D accordingly,) though members of his Peer-Review Panel might have been aware of his young Earth beliefs - their evaluation of his work was based on his actual research and not his personal beliefs.
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Displaying 1 - 8 of 8 reviews
January 16, 2023
4.5 stars because of some repetitiveness and typos.
It was so fascinating to learn about the Mandelbrot set as well as other patterns that so clearly display the glory of God. This book explains yet another reason that I love math- we get a glimpse of God's infinite beauty and creativity.
It was so fascinating to learn about the Mandelbrot set as well as other patterns that so clearly display the glory of God. This book explains yet another reason that I love math- we get a glimpse of God's infinite beauty and creativity.
July 19, 2022
Not being good at math, this book was a wild workout for my nearly nonexistent grey cells. I didn't understand most of it, but read it out of sheer stubbornness and then shock.
I had no idea. Nooooooo idea.
Good gracious.
The top of my head blew off and I'm not sure how to live without it.
I can't describe what I found out, but it shook me. I'm not kidding!
I recommend the book for sure, and also this documentary:
"Fractals: The Colors of Infinity" by Arthur C. Clarke - it's on Youtube
https://www.youtube.com/watch?v=WoHGl...
I had no idea. Nooooooo idea.
Good gracious.
The top of my head blew off and I'm not sure how to live without it.
I can't describe what I found out, but it shook me. I'm not kidding!
I recommend the book for sure, and also this documentary:
"Fractals: The Colors of Infinity" by Arthur C. Clarke - it's on Youtube
https://www.youtube.com/watch?v=WoHGl...
April 12, 2025
What a fascinating topic! When I say that I read the book, you should understand that I skimmed a lot of the scientific and mathematical concepts behind it.
The illustrations were fabulous. I lingered over them for quite a while, marveling at the beauty of patterns produced by mathematical formulas. I was particularly fascinated by the 3D representation of the Mandelbrot set, the Mandelbulb (p. 190), and the Menger sponge (p. 178), which looked like a Borg cube to me. I have to admit, I grew a little tired of the writing style of the author. There was a lot of repetition and even though I’m on his team, it became somewhat irritating to have him return to the same line time after time about how only the mind of God could create the mathematical laws of the universe. However, I certainly agree! The quotes he included in the last chapter by secular scientist Eugene Wigner were quite striking. Whether or not you agree that only the Christian God can be the mastermind behind fractals and math and Mandelbrots, Lisle raises some interesting questions that are worth contemplating. It’s an attractive, well illustrated book even if you disagree with the premise that Dr. Lisle takes about God.
The illustrations were fabulous. I lingered over them for quite a while, marveling at the beauty of patterns produced by mathematical formulas. I was particularly fascinated by the 3D representation of the Mandelbrot set, the Mandelbulb (p. 190), and the Menger sponge (p. 178), which looked like a Borg cube to me. I have to admit, I grew a little tired of the writing style of the author. There was a lot of repetition and even though I’m on his team, it became somewhat irritating to have him return to the same line time after time about how only the mind of God could create the mathematical laws of the universe. However, I certainly agree! The quotes he included in the last chapter by secular scientist Eugene Wigner were quite striking. Whether or not you agree that only the Christian God can be the mastermind behind fractals and math and Mandelbrots, Lisle raises some interesting questions that are worth contemplating. It’s an attractive, well illustrated book even if you disagree with the premise that Dr. Lisle takes about God.
December 13, 2023
Short version: Good explanations of facts, with theism shoehorned in in a really distasteful, scientifically irresponsible way. Come at me, you proponents of intelligent design. I have a graduate degree in physics too.
--
Remove the Bible-thumping, unscientific assertions and you have a pretty nice little coffee table book about fractals. Unfortunately, Lisle's theistic non sequiturs, repeated comments about the inability of non-Christian thinkers to reason properly, and final evangelical messaging distract quite a lot from the cool math stuff. I'd give it a 4/5 for the math and pictures, and a 1/5 for the sheer scientific hypocrisy.
Lisle's premise is that anything beautiful or complex must have been intelligently designed; his conclusion is that fractals are evidence of the Christian God. As an agnostic, I disagree with the premise, but I understand the desire for many to have an answer to the question, 'Why does this beautiful, complex thing exist?' I don't begrudge Lisle his view of the mysterious, but he holds up fractal beauty specifically as evidence that the Christian God, and no other god, truly exists in the universe. It's a gross violation of scientific principles to claim that something is evidence of God, and it's further extremely suspect when someone who purports to be a rational thinker then claims his own theistic philosophy to be the most logical one, and all others to be bunk.
The existence of God cannot be scientifically disproved because there is no testable condition that, when shown to be true, is evidence of God and nothing else ('X and Y are things that only happen when an omnipotent deity exists, therefore if I observe X or Y, the omnipotent deity exists'). The concept of an omnipotent deity is purposely evidence-avoidant. Thus, it's irresponsible for a scientist truly dedicated to their work to claim that God exists, and an abuse of evidence to argue that something (e.g. the shapes that mathematical expressions make when plotted) proves the existence of God when there's no logical foundation to support the argument.
I'm deeply disappointed that a person with a graduate degree in astrophysics from one of the best physics programs in the US seems to have missed the basic premise of science: truth is determined by physical evidence and sound logical reasoning. Nobody in STEM who has learned their discipline properly should consider intelligent design a superior argument to the theory of evolution for the origin of complex organisms, yet the author establishes himself as anti-evolution on the very first page of this book, prior to any discussion of numbers and fractals. It's one thing to look for signs of one's deity in the spaces between well-supported scientific theories, but it's another thing to reject scientific reasoning all together.
Creationism is not bad in and of itself, but to present oneself as a professional in science and then abandon scientific thinking is, at the very least, deceitful.
--
Remove the Bible-thumping, unscientific assertions and you have a pretty nice little coffee table book about fractals. Unfortunately, Lisle's theistic non sequiturs, repeated comments about the inability of non-Christian thinkers to reason properly, and final evangelical messaging distract quite a lot from the cool math stuff. I'd give it a 4/5 for the math and pictures, and a 1/5 for the sheer scientific hypocrisy.
Lisle's premise is that anything beautiful or complex must have been intelligently designed; his conclusion is that fractals are evidence of the Christian God. As an agnostic, I disagree with the premise, but I understand the desire for many to have an answer to the question, 'Why does this beautiful, complex thing exist?' I don't begrudge Lisle his view of the mysterious, but he holds up fractal beauty specifically as evidence that the Christian God, and no other god, truly exists in the universe. It's a gross violation of scientific principles to claim that something is evidence of God, and it's further extremely suspect when someone who purports to be a rational thinker then claims his own theistic philosophy to be the most logical one, and all others to be bunk.
The existence of God cannot be scientifically disproved because there is no testable condition that, when shown to be true, is evidence of God and nothing else ('X and Y are things that only happen when an omnipotent deity exists, therefore if I observe X or Y, the omnipotent deity exists'). The concept of an omnipotent deity is purposely evidence-avoidant. Thus, it's irresponsible for a scientist truly dedicated to their work to claim that God exists, and an abuse of evidence to argue that something (e.g. the shapes that mathematical expressions make when plotted) proves the existence of God when there's no logical foundation to support the argument.
I'm deeply disappointed that a person with a graduate degree in astrophysics from one of the best physics programs in the US seems to have missed the basic premise of science: truth is determined by physical evidence and sound logical reasoning. Nobody in STEM who has learned their discipline properly should consider intelligent design a superior argument to the theory of evolution for the origin of complex organisms, yet the author establishes himself as anti-evolution on the very first page of this book, prior to any discussion of numbers and fractals. It's one thing to look for signs of one's deity in the spaces between well-supported scientific theories, but it's another thing to reject scientific reasoning all together.
Creationism is not bad in and of itself, but to present oneself as a professional in science and then abandon scientific thinking is, at the very least, deceitful.
December 25, 2023
Truth be told, the math is far beyond my comprehension. But the pictures are gorgeous and the idea that math and beauty are built into the universe, and how the mathematical relation to reality corresponds to God is excellent. The images are gorgeous and related to the topic. It was a great read, even knowing I barely understand the whole topic.
October 25, 2022
This is a beautiful book with a very misleading subtitle.
Once upon a time, when electronic computers were new, I watched a printer rapidly spit out the numbers 1,1,2,3,5,8, … 832040, 1346269, 2178309,…. The numbers raced down the page, forming a dark triangle as the digits increased. These were the Fibonacci numbers, a sequence that has intrigued mathematicians for almost a millennium and certainly entranced the young high school student watching that printer.
There are many ways to attract people to the beauty of mathematics. I was intrigued by the Fibonacci sequence, the Cantor Set, and the distribution of prime numbers. Later in life I played with the Collatz Conjecture and other recursive sequences. At a math conference in the 1980s, I picked up a copy of Benoit Mandelbrot’s The Fractal Geometry of Nature, a book that displayed the beautiful chaotic self-similarity of Nature’s geometry. (Ask the question, “How long is this shoreline?” A serious attempt at an answer forces one to recognize that the length of a shoreline greatly depends on the resolution used by the one doing the measuring. Peninsulas include smaller points of land which just into the sea; bays include smaller bays with indentations within indentations.)
One example of a fractal, introduced by Mandelbrot himself, is created in the complex plane by iterating the quadratic function f(x) = x^2+c. Pick a complex number c and examine the sequence c, f(c), f(f(c)), and so on. Ask the question, “Do these iterates of the function form a bounded sequence?” If the sequence is bounded, then the complex number c is in the Mandelbrot set. In the complex plane, color the point c black. If the sequence c, f(c), f(f(c)),… is not bounded, give c a color based on the speed of growth of the sequence. Use a modern computer to color the points in the complex plane. With this coloring the mathematical analysis of the Mandelbrot set gives rise to intricate paintings of the complex plane.
Fractals, The Secret Code of Creation, by Jason Lisle, is a beautifully crafted coffee-table book which invites readers not just to the beauty of mathematics but to belief in Christianity. The book does a good job of introducing one particular fractal example the Mandelbrot set. But the jump to Christianity is forced. Yes, the infinite complexity of the Mandelbrot set is beautiful. Many mathematicians agree that beautiful objects like this are independent of human thought. (This belief is mathematical platonism.) But the leap from mathematical platonism to belief in a creator and then to belief in the Biblical God is not obvious and is poorly argued in this book.
The book has twelve chapters. Nine of these are mathematical, with beautiful photos and well-written text. Written for a popular audience, the prose is simple and easy to follow. Difficult mathematical concepts are lightly sketched and invite the reader to enjoy the mathematics displayed by the pictures.
The mathematical chapters are well done, but the book is really an apologetic for the Christian worldview. It argues that mathematics, particularly the Mandelbrot fractal and similar objects, display God’s nature. The first chapter, The Secret Code, claims that “those who reject God like to explain the complexity of biological life by appealing to Darwinian evolution” but mathematics is free from this “because numbers do not evolve.” The fractals in this book, beginning with the Mandelbrot set give an “infinitesimal glimpse into the mind of God” (p. 9.) These first few pages set the stage for a reoccurring theme: there are two competing worldviews, the Christian worldview and those who do not believe in the Christian God. The mathematics of fractals is to lead the reader towards the Christian worldview.
After this introduction, the book describes the required mathematical material: sets, complex numbers, function iteration. The mathematical descriptions are well done and intended for a popular audience. There are no frightening equations to drive away the reader. The prose, along with the accompanying artwork, is inviting. One might use much of this book as an invitation into the study of mathematics. Indeed, many mathematicians have used the study of fractals to do just that. (Search the internet for the Fractal Foundation, as an example.)
Chapters two through seven are all about the mathematics of the Mandelbrot set, text printed over elegant colorful pictures of various regions of the fractals. Chapters two through five, with picturesque titles Valley of the Seahorses, Valley of the Double Spirals, Infinite Elephants, Scepters on Seahorses focus on a particular region of the Mandelbrot set, zooming in to display intricate spirals, bays, peninsulas. Yes, indeed, the infinite complexity of these drawings is beautiful and does agree with my belief that mathematics is the language of The Great Artist.
The chapter, Changing the Formula, asks what happens if the simple quadratic f(x)=x^2+c is replaced by other quadratics. It is shown, by example, that other quadratics merely transform the Mandelbrot set, shifting it in some way. (A math student comfortable with function transformations will recognize that any quadratic function can be transformed into any other quadratic — this is the essence of the quadratic formula — and so it should not be surprising that nothing new is achieved by replacing one quadratic by another.)
Chapters seven, nine, and ten (Multibrots, The Tricorn, The Sine Function) replace a quadratic function first by other polynomials, then by functions involving fractional exponents, then by a conjugate function and finally by trigonometric and exponential functions. Euler’s marvelous identity about e^iz briefly comes into play, linking trigonometric and exponential functions in the complex plane. In all of these chapters, the mathematical explanations are kept clear and simple and the beautiful artwork continues. The eleventh chapter, Geometric and 3D Fractals, asks about higher dimensional figures. It introduces the quaternions. The chapter does not go deeply into the material but is intended to leave the reader curious and intrigued.
Chapter 8, Fractals and the Christian Worldview, is an interlude to the mathematics. That chapter, and the final chapter, Physical Fractals and the Grand Dilemma, argue that fractals should lead people to the Christian God. The last chapter describes occurrences of fractals as physical objects in nature (shorelines, clouds, trees, etc.) returning to the initial topic in Mandelbrot’s introductory book. The book ends with a gospel presentation.
Would I put this book on my coffee table? Probably not…. The flaw in the apologetics is that mathematical platonism, argued in the book, does not immediately point to a Christian worldview. While most of my mathematical colleagues would identify with mathematical platonism, their religious views vary from atheism/agnosticism through various religions like Judaism or Islam. The leap from “these objects exist outside human thought” to “they prove a Christian worldview" will leave a thoughtful skeptic with whiplash.
Some of my house guests are not Christians; I would be concerned that the book’s simplistic and dismissive statements of atheism and other religions would offend, but I could mitigate that somewhat to promote discussion.
My main concern would be with my Christian houseguests. The author, Dr. Jason Lisle, is affiliated with Answers in Genesis and is founder of the Bible Science Institute, both of which insist on a Young Earth interpretation of Genesis 1-3. Lisle rejects the Big Bang theory and, by misinterpreting various challenges to modern cosmology, incorrectly claims that many scientists reject the Big Bang. While Lisle’s Young Earth Creationism does not appear in this book, I am not sure I want a house guest to assume that I agree with Lisle’s interpretation of Genesis or his interpretation of science. Ironically, this beautiful book on fractals makes it clear that elegant and complex structures can arise from very simple processes. This is a concept that underlies the theory of evolution, which Lisle opposes.
This is a beautiful book on the beauty of mathematics. The photos and mathematical descriptions are excellent and intriguing. The book is weakest when it claims that this beauty leads to the Christian gospel. My arguments for the validity of Christianity take a different route.
Once upon a time, when electronic computers were new, I watched a printer rapidly spit out the numbers 1,1,2,3,5,8, … 832040, 1346269, 2178309,…. The numbers raced down the page, forming a dark triangle as the digits increased. These were the Fibonacci numbers, a sequence that has intrigued mathematicians for almost a millennium and certainly entranced the young high school student watching that printer.
There are many ways to attract people to the beauty of mathematics. I was intrigued by the Fibonacci sequence, the Cantor Set, and the distribution of prime numbers. Later in life I played with the Collatz Conjecture and other recursive sequences. At a math conference in the 1980s, I picked up a copy of Benoit Mandelbrot’s The Fractal Geometry of Nature, a book that displayed the beautiful chaotic self-similarity of Nature’s geometry. (Ask the question, “How long is this shoreline?” A serious attempt at an answer forces one to recognize that the length of a shoreline greatly depends on the resolution used by the one doing the measuring. Peninsulas include smaller points of land which just into the sea; bays include smaller bays with indentations within indentations.)
One example of a fractal, introduced by Mandelbrot himself, is created in the complex plane by iterating the quadratic function f(x) = x^2+c. Pick a complex number c and examine the sequence c, f(c), f(f(c)), and so on. Ask the question, “Do these iterates of the function form a bounded sequence?” If the sequence is bounded, then the complex number c is in the Mandelbrot set. In the complex plane, color the point c black. If the sequence c, f(c), f(f(c)),… is not bounded, give c a color based on the speed of growth of the sequence. Use a modern computer to color the points in the complex plane. With this coloring the mathematical analysis of the Mandelbrot set gives rise to intricate paintings of the complex plane.
Fractals, The Secret Code of Creation, by Jason Lisle, is a beautifully crafted coffee-table book which invites readers not just to the beauty of mathematics but to belief in Christianity. The book does a good job of introducing one particular fractal example the Mandelbrot set. But the jump to Christianity is forced. Yes, the infinite complexity of the Mandelbrot set is beautiful. Many mathematicians agree that beautiful objects like this are independent of human thought. (This belief is mathematical platonism.) But the leap from mathematical platonism to belief in a creator and then to belief in the Biblical God is not obvious and is poorly argued in this book.
The book has twelve chapters. Nine of these are mathematical, with beautiful photos and well-written text. Written for a popular audience, the prose is simple and easy to follow. Difficult mathematical concepts are lightly sketched and invite the reader to enjoy the mathematics displayed by the pictures.
The mathematical chapters are well done, but the book is really an apologetic for the Christian worldview. It argues that mathematics, particularly the Mandelbrot fractal and similar objects, display God’s nature. The first chapter, The Secret Code, claims that “those who reject God like to explain the complexity of biological life by appealing to Darwinian evolution” but mathematics is free from this “because numbers do not evolve.” The fractals in this book, beginning with the Mandelbrot set give an “infinitesimal glimpse into the mind of God” (p. 9.) These first few pages set the stage for a reoccurring theme: there are two competing worldviews, the Christian worldview and those who do not believe in the Christian God. The mathematics of fractals is to lead the reader towards the Christian worldview.
After this introduction, the book describes the required mathematical material: sets, complex numbers, function iteration. The mathematical descriptions are well done and intended for a popular audience. There are no frightening equations to drive away the reader. The prose, along with the accompanying artwork, is inviting. One might use much of this book as an invitation into the study of mathematics. Indeed, many mathematicians have used the study of fractals to do just that. (Search the internet for the Fractal Foundation, as an example.)
Chapters two through seven are all about the mathematics of the Mandelbrot set, text printed over elegant colorful pictures of various regions of the fractals. Chapters two through five, with picturesque titles Valley of the Seahorses, Valley of the Double Spirals, Infinite Elephants, Scepters on Seahorses focus on a particular region of the Mandelbrot set, zooming in to display intricate spirals, bays, peninsulas. Yes, indeed, the infinite complexity of these drawings is beautiful and does agree with my belief that mathematics is the language of The Great Artist.
The chapter, Changing the Formula, asks what happens if the simple quadratic f(x)=x^2+c is replaced by other quadratics. It is shown, by example, that other quadratics merely transform the Mandelbrot set, shifting it in some way. (A math student comfortable with function transformations will recognize that any quadratic function can be transformed into any other quadratic — this is the essence of the quadratic formula — and so it should not be surprising that nothing new is achieved by replacing one quadratic by another.)
Chapters seven, nine, and ten (Multibrots, The Tricorn, The Sine Function) replace a quadratic function first by other polynomials, then by functions involving fractional exponents, then by a conjugate function and finally by trigonometric and exponential functions. Euler’s marvelous identity about e^iz briefly comes into play, linking trigonometric and exponential functions in the complex plane. In all of these chapters, the mathematical explanations are kept clear and simple and the beautiful artwork continues. The eleventh chapter, Geometric and 3D Fractals, asks about higher dimensional figures. It introduces the quaternions. The chapter does not go deeply into the material but is intended to leave the reader curious and intrigued.
Chapter 8, Fractals and the Christian Worldview, is an interlude to the mathematics. That chapter, and the final chapter, Physical Fractals and the Grand Dilemma, argue that fractals should lead people to the Christian God. The last chapter describes occurrences of fractals as physical objects in nature (shorelines, clouds, trees, etc.) returning to the initial topic in Mandelbrot’s introductory book. The book ends with a gospel presentation.
Would I put this book on my coffee table? Probably not…. The flaw in the apologetics is that mathematical platonism, argued in the book, does not immediately point to a Christian worldview. While most of my mathematical colleagues would identify with mathematical platonism, their religious views vary from atheism/agnosticism through various religions like Judaism or Islam. The leap from “these objects exist outside human thought” to “they prove a Christian worldview" will leave a thoughtful skeptic with whiplash.
Some of my house guests are not Christians; I would be concerned that the book’s simplistic and dismissive statements of atheism and other religions would offend, but I could mitigate that somewhat to promote discussion.
My main concern would be with my Christian houseguests. The author, Dr. Jason Lisle, is affiliated with Answers in Genesis and is founder of the Bible Science Institute, both of which insist on a Young Earth interpretation of Genesis 1-3. Lisle rejects the Big Bang theory and, by misinterpreting various challenges to modern cosmology, incorrectly claims that many scientists reject the Big Bang. While Lisle’s Young Earth Creationism does not appear in this book, I am not sure I want a house guest to assume that I agree with Lisle’s interpretation of Genesis or his interpretation of science. Ironically, this beautiful book on fractals makes it clear that elegant and complex structures can arise from very simple processes. This is a concept that underlies the theory of evolution, which Lisle opposes.
This is a beautiful book on the beauty of mathematics. The photos and mathematical descriptions are excellent and intriguing. The book is weakest when it claims that this beauty leads to the Christian gospel. My arguments for the validity of Christianity take a different route.
January 8, 2024
Author’s point: Mathematics and specifically the Mandelbrot Set contain a secret, infinite, and beautiful code that represents the mind of the Trinity.
My evaluation: As I am eager to find signs that point me in the direction of infinity and scents that excite my spiritual curiosity and imagination, the Mandelbrot Set inspires me with the spiritual hope to see God. The effect of this book was similar to The Divine Comedy.
My evaluation: As I am eager to find signs that point me in the direction of infinity and scents that excite my spiritual curiosity and imagination, the Mandelbrot Set inspires me with the spiritual hope to see God. The effect of this book was similar to The Divine Comedy.
September 19, 2022
Wish I read this during my mid-high school years.
Displaying 1 - 8 of 8 reviews