Lissajous Curves Lissajous curves are created by plotting two oscillations on perpendicular axes and ​​​. These oscillations, represented by sinusoidal functions, intersect to create different patterns. When the ratio of these frequencies is equal to — the oscillations are equally phased— the curve is a straight line.

In this blog post, we will dive into the fascinating world of coin flip sequences. Leveraging the capabilities of R, we will conduct simulations to gain insights into the probabilities of consecutive sequences of heads or tails. Let’s kick things off by simulating coin flips using R. We’ll conduct experiments with varying numbers of flips to observe how the results evolve.

Top Trumps is a card game for children. The mind can wander when playing such games with kids… typically, I start thinking: what is the best strategy for this game? But also, as the game drags on: what is the quickest way to lose? Since Top Trumps is based on numerical values with simple outcomes, it seemed straightforward to analyse the cards and to simulate different scenarios to look at these questions.

Steganone is an unusual natural product, known for about 40 years now. The assignment of its absolute configurations makes for an interesting, on occasion rather confusing, and perhaps not entirely atypical story. I will start with the modern accepted stereochemical structure of this molecule, which comes in the form of two separately isolable atropisomers.

The text books say that cyclohexenone A will react with a Grignard reagent by delivery of an alkyl (anion) to the carbon of the carbonyl ( 1,2-addition ) but if dimethyl lithium cuprate is used, a conjugate 1,4-addition proceeds, to give the product B shown below.

In the preceding post, I described a fascinating experiment and calculation by Bogle and Singleton, in which the trajectory distribution of molecules emerging from a single transition state was used to rationalise the formation of two isomeric products 2 and **3. ** In the present post, I explore possible consequences of including a sodium cation (X=Na ⁺ below) in the computational