In the pictures below, the Collatz map fractal includes parts resembling the Mandelbrot set. Why? Do other fractals do so?
The Mandelbrot set
From Wikimedia Commons
Part of the Collatz map fractal
From Wikimedia Commons
2026-03-27 20:31:25.1774643485
Why does the Mandelbrot shape show up in other fractals?
2.1k Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in COMPLEX-NUMBERS
- Value of an expression involving summation of a series of complex number
- Minimum value of a complex expression involving cube root of a unity
- orientation of circle in complex plane
- Locus corresponding to sum of two arguments in Argand diagram?
- Logarithmic function for complex numbers
- To find the Modulus of a complex number
- relation between arguments of two complex numbers
- Equality of two complex numbers with respect to argument
- Trouble computing $\int_0^\pi e^{ix} dx$
- Roots of a complex equation
Related Questions in FRACTALS
- does the area converge?
- "Mandelbrot sets" for different polynomials
- Is the Mandelbrot set path-connected?
- Does the boundary of the Mandelbrot set $M$ have empty interior?
- What sort of function is this? (Logistic map?)
- effective degree for normalized escape-time of hybrids
- Julia set of $x_n = \frac{ x_{n-1}^2 - 1}{n}$
- A closed form for the sum $\sum_{s=0}^{n-1} e^{\frac{s(s+1)}{2}i\theta}$?
- Given a real number $d , (1<d<2)$, is there a fractal with fractal dimension $d$?
- How can one write a line element for non-integer dimensions?
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
This resemblance, of which I see only a bit of, is likely due to the fact that both are fractals generated on the complex plane by convergence of non-trivial equations (to distinguish them form fractals like Sierpinski's Triangle/Sponge/Carpet or Koch's Snowflake that are generated geometrically); they both share similarities with Julia Sets. Since the fractals are self-similar, the nodules of similarity are likely to show up, and the human brain picks up patterns and highlights the similarities between patterns, making instances where the dynamics of the two fractals are vaguely similar stand out, even if the actual similarities are weak.