Has there been a significant tie made between group theory and fractal geometry? What are some ways that they have been tied together? I've been inspired to ask this question by this image of a free group.
2026-03-29 04:10:56.1774757456
H0w have group theory and fractal geometry been combined?
2.2k Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in GROUP-THEORY
- What is the intersection of the vertices of a face of a simplicial complex?
- Group with order $pq$ has subgroups of order $p$ and $q$
- How to construct a group whose "size" grows between polynomially and exponentially.
- Conjugacy class formula
- $G$ abelian when $Z(G)$ is a proper subset of $G$?
- A group of order 189 is not simple
- Minimal dimension needed for linearization of group action
- For a $G$ a finite subgroup of $\mathbb{GL}_2(\mathbb{R})$ of rank $3$, show that $f^2 = \textrm{Id}$ for all $f \in G$
- subgroups that contain a normal subgroup is also normal
- Could anyone give an **example** that a problem that can be solved by creating a new group?
Related Questions in SOFT-QUESTION
- Reciprocal-totient function, in term of the totient function?
- Ordinals and cardinals in ETCS set axiomatic
- Does approximation usually exclude equality?
- Transition from theory of PDEs to applied analysis and industrial problems and models with PDEs
- Online resources for networking and creating new mathematical collaborations
- Random variables in integrals, how to analyze?
- Could anyone give an **example** that a problem that can be solved by creating a new group?
- How do you prevent being lead astray when you're working on a problem that takes months/years?
- Is it impossible to grasp Multivariable Calculus with poor prerequisite from Single variable calculus?
- A definite integral of a rational function: How can this be transformed from trivial to obvious by a change in viewpoint?
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?
Related Questions in GEOMETRIC-GROUP-THEORY
- Clarification of proof of generating set from fundamental domain
- Does $SL_2(\mathbb{Z}[\sqrt{2}])$ have a finite presentation?
- Making linear groups trivial by adding an equal number of generators and relations
- Is There any quasi-isomorphism between $\mathbb{R}$ and $\mathbb{R}^2$?
- Polynomially sized Folner sets
- Boundary $\partial F_n$ of a free group $F_n$
- Geodesic ray converges to infinity
- Boundary of the Hyperbolic plane homeomorphic to S1
- 3D representation of A4 that preserves the unit ball
- Finite index subgroups in Amalgamated Free products
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?
There are a lot of connections in geometric group theory, which studies things like free groups. Every hyperbolic group (an infinite group with a special condition) has a space at infinity that is either a sphere or a fractal. For instance, the free group has a cantor set at infinity. Other groups have Sierpinski curves and Menger sponges.
Space-filling curves also arise in hyperbolic geometry (see the Cannon-Thurston map).
Finally, most fractals can be generated using the ring structure of $\mathbb{C}$.