Recent content by Sorento7

We know that a Clifford torus is parameterized in 4D euclidean space by: (x1,x2,x3,x4) = (Sin(theta1), Cos(theta1), Sin(theta2), Cos(theta2)) {0<=theta1 and theta2<2pi} Consider that a clifford torus is the immediate result of Circle * Circle Now, have you encountered a similar manifold...

No solution?:frown:

You can also think of creation of universe and evolution, simplest subatomic structures changing to an intelligent human being with key contribution of genetic mutations. I think that makes sense. (However, philosophically speaking, I think a concept such as Mandelbrot's fractal did exist...

Good point on the impact of rounding errors on final shape. But this only changes the question without answering it, why should this simple set introduce such weird rounding errors producing a fractal?

Thanks. That was helpful:approve:

Suppose: F(\vec{a}) = (1/\vec{a}.\vec{b}) \vec{a} dot is the Euclidean inner product and F is defined as a vector space(R3 → R3) I need ∂\vec{F}/∂\vec{a} (given that \vec{b} is an arbitrary constant vector.)

Maybe I phrased it wrong. Its the result of multiplying inversion of an inner product to one of its vector components. (1/\vec{a}.\vec{b}) * \vec{a} edit: \vec{b} is a constant vector.

Homework Statement A(\vec{x}) = (F + T * x )2 F is a constant, x is a 2×1 vector T is a (constant) 1×2 matrixB(\vec{x}) = || K.Z.x ||2 k:3\times3 matrix and Z:3\times2, x the same as aboveB(x) is also R2→RC(x) = A(x) + B(x) Homework Equations 1- I am confused...

no answer? wow I thought that should have been an easy differentiation?

These explanations are quite correct, but I don't think that chaos can explain the repetetive patterns in Mandelbrot which are very "similar" and very "different" at the same time. Transitions of these patterns everywhere in plane happens smoothly, and the whole shape is replicated in bizarre...

I am working on a software for analysis of brain connections using MRI. Please suggest the simplest way to find a vector which is: perpendicular to a unit vector that is positioned in the coordinate center, it should be in the 2D plane containing the given vector and a given point on...

[SIZE="6"]\frac{∂ \frac{\vec{a}}{ \vec{a} . \vec{b}} }{∂\vec{a}}

Homework Statement \frac{∂ \frac{\vec{a}}{ \vec{a} . \vec{b}} }{∂\vec{a}} b is not a function of a Homework Equations I want to differentiate this, (the jacobian of the vector field) dot is the Euclidean inner product.The Attempt at a Solution \acute{u}.v -...

Do you know why a simple set used for construction of the Mandelbrot's fractal results in a jaw dropping shape?

Thanks this sheds some light. Forgive my rudimentary mistakes since I am actually a doctor! Well, the problem was more complicated than I described: A(x) = (F(x) - M(x) + ∂M/∂x * x )2 taking 3*1 vector x to scalar B(x) = || K.x ||2 k:3*3 matrix I am confused how...