This method of swirling was donated to us by Gabbie. 

Here's the soap recipe l used:

• Olive oil 275g
• Palm oil 250g
• Coconut oil 250g
• Rice bran oil 100g
• Canola oil 100g
• Castor oil 25g
• Purple ultramarine 1 teaspoon (diluted in a small amount of oil or water)
• Ttitanium dioxide 1 teaspoon (blended in a small amount of oil)
• 30mls Lavender essential oil
• Water 312mls
• Sodium hydroxide 138.5g (discounted at 7%)

Instructions:
(Basic instructions on the coathanger swirl were first found here:http://www.latheringsforum.com/bb/viewtopic.php?t=6516&postdays=0&postorder=asc&highlight=hanger&start=15
what follows is merely my interpretation.)

l'm not usually very good at swirling because l always soap too warm, and use the stickblender for too long. This makes for a quite thick 'trace' that doesn't lend itself to swirling, but rather being 'heavily poured' into the mould, and spread around. for this recipe, l let the oils and lye go almost stone cold before making the soap. l didn't want to give it any excuse to thicken up, you want a nice runny consistency.
Measure all your hard oils and melt them gently, then add your cold oils, and let it all cool.
Measure your cold water, and carefully add the sodium hydroxide, stirring gently.  Let this cool right down also.
Dilute the purple colour, and set it to one side in a large pyrex jug. The titanium dioxide l mixed in with the warm soaping oils as they cooled.
I'd already altered my coathanger with a pair of pliers. The straight sides are so it would fit into a smaller log mould:
I then mixed the lye and oils with a stickblender in short bursts.  As soon as the soap emulsified or got to that beautiful glossy 'almost trace' like stage, l put the stickblender down and didn't touch it again.
The batter was still very thin.  There was a very faint pour line if you lifted the spoon above the soap & drizzled, but nothing like what l normally experience. lt was like very thin cream and sunk back into the surface quickly.
l added my fragrance (lavender essential oil) and stirred with a spatula.
I then split the batch in half and coloured one half purple.
l then started pouring the purple and white soap into the mould in alternate thin layers. l used my wooden log mould, and had it lined and ready to go.
First up was a thin layer of white soap along the bottom, about a centimetre's worth. Because the soap was still very runny, when l started the purple layer, l poured it over the back of a spatula.  If l'd poured straight into the mould l think it would have sunk completely to the bottom instead of forming 'stripes'. I continued pouring, alternating colours and always over the back of a spatula so that the stripes stayed roughly 'on top' of each other. Keep layering the two colours until you run out of soap mix.
Once the mould is full, insert the coathanger into the mould right to the bottom.
Because it was only my first time, l wasn't sure which way to swirl with the hanger.  Should it be from side to side, or up and down? l decided on mostly up and down, and zig zagged in a //// pattern from one long edge of the mould across to the other. l then added in one 'side to side' 'z' movement just in case, and pulled the coathanger straight out.
Overall l didn't swirl too much at all.  l'm no expert, but l figured the more l fiddled around with it, the more l would be blending the two colours, and l wanted them to be quite distinct, not a muddy third colour.
Then l put the soap to bed as per usual, and cut it 24 hours later.