Walk (four legs, in place)

The walk of the game cycles for four legs: the back-left and front-right paws step together, then the back-right and front-left, the stride fitted to a speed setting so no planted paw ever slides.

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What it is for

Walk (four legs, in place) is the walk of the nine game cycles, written for the fours set: four legs, numbered back-left, back-right, front-left and front-right. The gait has the legs stepping in diagonal pairs, which the program's own phase numbers confirm: the back-left and front-right paws share one half of the loop, the back-right and front-left share the other, the ordinary walking trot of a four-legged animal.

The principle it shows: arcs

The body's height still comes from the same cosine formula the two-legged walk uses, worked out from the lower leg's own bending angle rather than drawn by hand. With four legs sharing the load two at a time instead of one, that height formula only has to compare one diagonal pair against the other, which is why a four-legged walk can hold a steadier body height than a two-legged one does over the same stride.

The program, line by line

settings: speed = 0.75, h = 540, leg = 0.33, every = (clamp(0.9 - 0.3*speed, 0.45, 0.8)), stride = (57.29578*((clamp(speed*every/(4*leg), 0, 0.6)) + pow(clamp(speed*every/(4*leg), 0, 0.6), 3)/6 + 3*pow(clamp(speed*every/(4*leg), 0, 0.6), 5)/40)), give = 6, bend = 30, feet = 0.4
when it starts
  show the side view
  walk cycle every (every) s · arm swing 0 · no bob · roll 0.6 · stride (stride) · give (give) · bend (bend) · seen from the side
  back left foot follows (-feet*(stride*((1 - 4*mod(local/every + 0, 1))*(1 - step(0.5, mod(local/every + 0, 1))) + (4*mod(local/every + 0, 1) - 3)*step(0.5, mod(local/every + 0, 1))) + (give*(1 - step(0.5, mod(local/every + 0, 1))) + bend*step(0.5, mod(local/every + 0, 1)))*sin(pi*(2*mod(local/every + 0, 1) - step(0.5, mod(local/every + 0, 1))))))
  back right foot follows (-feet*(stride*((1 - 4*mod(local/every + 0.5, 1))*(1 - step(0.5, mod(local/every + 0.5, 1))) + (4*mod(local/every + 0.5, 1) - 3)*step(0.5, mod(local/every + 0.5, 1))) + (give*(1 - step(0.5, mod(local/every + 0.5, 1))) + bend*step(0.5, mod(local/every + 0.5, 1)))*sin(pi*(2*mod(local/every + 0.5, 1) - step(0.5, mod(local/every + 0.5, 1))))))
  front left foot follows (-feet*(stride*((1 - 4*mod(local/every + 0.5, 1))*(1 - step(0.5, mod(local/every + 0.5, 1))) + (4*mod(local/every + 0.5, 1) - 3)*step(0.5, mod(local/every + 0.5, 1))) + (give*(1 - step(0.5, mod(local/every + 0.5, 1))) + bend*step(0.5, mod(local/every + 0.5, 1)))*sin(pi*(2*mod(local/every + 0.5, 1) - step(0.5, mod(local/every + 0.5, 1))))))
  front right foot follows (-feet*(stride*((1 - 4*mod(local/every + 0, 1))*(1 - step(0.5, mod(local/every + 0, 1))) + (4*mod(local/every + 0, 1) - 3)*step(0.5, mod(local/every + 0, 1))) + (give*(1 - step(0.5, mod(local/every + 0, 1))) + bend*step(0.5, mod(local/every + 0, 1)))*sin(pi*(2*mod(local/every + 0, 1) - step(0.5, mod(local/every + 0, 1))))))
  dy follows (h*leg/2*(2 - (1 - step(0.5, mod(local/every, 1)))*(cos((stride*((1 - 4*mod(local/every + 0, 1))*(1 - step(0.5, mod(local/every + 0, 1))) + (4*mod(local/every + 0, 1) - 3)*step(0.5, mod(local/every + 0, 1))))*pi/180) + cos(((stride*((1 - 4*mod(local/every + 0, 1))*(1 - step(0.5, mod(local/every + 0, 1))) + (4*mod(local/every + 0, 1) - 3)*step(0.5, mod(local/every + 0, 1)))) + ((give*(1 - step(0.5, mod(local/every + 0, 1))) + bend*step(0.5, mod(local/every + 0, 1)))*sin(pi*(2*mod(local/every + 0, 1) - step(0.5, mod(local/every + 0, 1))))))*pi/180)) - step(0.5, mod(local/every, 1))*(cos((stride*((1 - 4*mod(local/every + 0.5, 1))*(1 - step(0.5, mod(local/every + 0.5, 1))) + (4*mod(local/every + 0.5, 1) - 3)*step(0.5, mod(local/every + 0.5, 1))))*pi/180) + cos(((stride*((1 - 4*mod(local/every + 0.5, 1))*(1 - step(0.5, mod(local/every + 0.5, 1))) + (4*mod(local/every + 0.5, 1) - 3)*step(0.5, mod(local/every + 0.5, 1)))) + ((give*(1 - step(0.5, mod(local/every + 0.5, 1))) + bend*step(0.5, mod(local/every + 0.5, 1)))*sin(pi*(2*mod(local/every + 0.5, 1) - step(0.5, mod(local/every + 0.5, 1))))))*pi/180))) - 0.01*h)
  sin wave on head · every (every/2) s · amp 2 · phase 0.6
  sin wave on tail · every (every) s · amp 10 · phase 1.2

• show the side view — the move is drawn in profile.
• set head -6, tail 20 — the head tips down a little and the tail lifts, the resting carry of a walking four-legged body.
• walk cycle every (every) s · arm swing 0 · no bob · roll 0.6 · stride (stride) · give (give) · bend (bend) · seen from the side — the base gait: a small 0.6-degree body roll timed to the stride.
• back left foot follows (…), back right foot follows (…), front left foot follows (…), front right foot follows (…) — each paw drags back through its own stance; the back-left and front-right share one half of the loop, the back-right and front-left the other, the diagonal pairing of a trot.
• dy follows (…) — the body sits at whichever diagonal pair is lower at that instant, dipping more at the middle of each step.
• sin wave on head · every (every/2) s · amp 2 · phase 0.6 — the head bobs twice a stride.
• sin wave on tail · every (every) s · amp 10 · phase 1.2 — the tail sways once a stride.

Written out in full, exactly as the engine prints them:

clamp(0.9 - 0.3*speed, 0.45, 0.8)

57.29578*((clamp(speed*every/(4*leg), 0, 0.6)) + pow(clamp(speed*every/(4*leg), 0, 0.6), 3)/6 + 3*pow(clamp(speed*every/(4*leg), 0, 0.6), 5)/40)

-feet*(stride*((1 - 4*mod(local/every + 0, 1))*(1 - step(0.5, mod(local/every + 0, 1))) + (4*mod(local/every + 0, 1) - 3)*step(0.5, mod(local/every + 0, 1))) + (give*(1 - step(0.5, mod(local/every + 0, 1))) + bend*step(0.5, mod(local/every + 0, 1)))*sin(pi*(2*mod(local/every + 0, 1) - step(0.5, mod(local/every + 0, 1)))))

-feet*(stride*((1 - 4*mod(local/every + 0.5, 1))*(1 - step(0.5, mod(local/every + 0.5, 1))) + (4*mod(local/every + 0.5, 1) - 3)*step(0.5, mod(local/every + 0.5, 1))) + (give*(1 - step(0.5, mod(local/every + 0.5, 1))) + bend*step(0.5, mod(local/every + 0.5, 1)))*sin(pi*(2*mod(local/every + 0.5, 1) - step(0.5, mod(local/every + 0.5, 1)))))

h*leg/2*(2 - (1 - step(0.5, mod(local/every, 1)))*(cos((stride*((1 - 4*mod(local/every + 0, 1))*(1 - step(0.5, mod(local/every + 0, 1))) + (4*mod(local/every + 0, 1) - 3)*step(0.5, mod(local/every + 0, 1))))*pi/180) + cos(((stride*((1 - 4*mod(local/every + 0, 1))*(1 - step(0.5, mod(local/every + 0, 1))) + (4*mod(local/every + 0, 1) - 3)*step(0.5, mod(local/every + 0, 1)))) + ((give*(1 - step(0.5, mod(local/every + 0, 1))) + bend*step(0.5, mod(local/every + 0, 1)))*sin(pi*(2*mod(local/every + 0, 1) - step(0.5, mod(local/every + 0, 1))))))*pi/180)) - step(0.5, mod(local/every, 1))*(cos((stride*((1 - 4*mod(local/every + 0.5, 1))*(1 - step(0.5, mod(local/every + 0.5, 1))) + (4*mod(local/every + 0.5, 1) - 3)*step(0.5, mod(local/every + 0.5, 1))))*pi/180) + cos(((stride*((1 - 4*mod(local/every + 0.5, 1))*(1 - step(0.5, mod(local/every + 0.5, 1))) + (4*mod(local/every + 0.5, 1) - 3)*step(0.5, mod(local/every + 0.5, 1)))) + ((give*(1 - step(0.5, mod(local/every + 0.5, 1))) + bend*step(0.5, mod(local/every + 0.5, 1)))*sin(pi*(2*mod(local/every + 0.5, 1) - step(0.5, mod(local/every + 0.5, 1))))))*pi/180))) - 0.01*h

Try this

1. Raise the walking speed from 0.75 to 1.75 body heights a second, the top of this move's fitted range. The diagonal pairs quicken and lengthen their stride together, without a planted paw sliding.

   In the program: params.speed 0.75 → 1.75

2. Turn each stance paw only a tenth of the way flat instead of four-tenths. The walk looks lighter on its paws, each step leaving less of a trailing drag.

   In the program: params.feet 0.4 → 0.1

How it differs from Walk (in place) and Run (four legs, in place)

Walk (in place) is the two-legged version, one foot down at a time rather than a diagonal pair. Run (four legs, in place) is this same diagonal-pair mechanism pushed to a faster, wider bound.

Works on

c4c:beh:cycle_walk_fours · version 1.0.0 · c4c-free · by Jabbertoon