Messages

1

Presentations and discussions / Julia Set

« on: March 15, 2017, 06:07:38 PM »

Turns out that there are 4D analogues to the 2D Julia sets which use quaternions ($i^2 = j^2 = k^2 = ijk = -1$) instead of regular complex numbers. Seeing as they're 4D they can only be visualised as 3D slices of the whole set, which end up looking quite a bit different than the regular Julia sets depending on the chosen slice.

Here's a link to a video which passes through multiple 3D slices of a quaternion Julia set: https://www.youtube.com/watch?v=VkmqT6MQoDE
And bellow is an image of such a slice.

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HA2 / Re: HA2 problem 2

« on: January 27, 2015, 09:40:25 PM »

But in that case it asks us to find the general solution of v by using the general solution of v, which doesn't make ant sense.

No, it asks to find the general solution $u$ of the original equation by using the general solution $v$ of the reduced equation. --V.I.

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HA2 / HA2 problem 2

« on: January 27, 2015, 08:57:40 PM »

I was wondering whether there might be a typo in problem 2.2 as otherwise, we are asked to solve for v from its general solution but without being given any boundary or initial conditions.

No -- just find the general solution. V.I.